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Algebra 2 Unit 12: Trigonometry
This unit includes 96 pages of guided notes, homework assignments, three quizzes, two study guides, and two unit tests that cover the topics listed in the description below.
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This unit contains the following topics:
Part I: • Pythagorean Theorem • Special Right Triangles • Trigonometric Functions (sin, cos, tan, csc, sec, cot) • Finding Side and Angle Measures • Applications: Angle of Elevation and Depression • Angles in Standard Position • Converting between Degrees and Radians • Coterminal and Reference Angles • Trigonometric Functions in the Coordinate Plane • The Unit Circle • Law of Sines • Law of Cosines • Area of Triangles • Applications of Law of Sines, Law of Cosines, and Area
Unit 12 Part II: • Graphing Trigonometric Functions • Trigonometric Identities • Sum and Difference of Angle Identities • Double-Angle and Half-Angle Identities • Solving Trigonometric Equations
Note: Due to the length of this unit, it is divided into two parts with two unit tests.
This unit does not contain activities.
This is the guided notes, homework assignments, quizzes, study guide, and unit test only. For suggested activities to go with this unit, check out the ATA Activity Alignment Guides .
This resource is included in the following bundle(s):
Algebra 2 Curriculum
License Terms:
This purchase includes a single non-transferable license, meaning it is for one teacher only for personal use in their classroom and can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. A t ransferable license is not available for this resource.
Copyright Terms:
No part of this resource may be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.
What standards is this curriculum aligned to?
What format are the files in, will i have access to materials if they are updated, are answer keys included, are videos included.
All things algebra is the best math creator in my opinion, I will continuously use and purchase the products! Students find them easy to use, engaging, and fun! I love the opportunities for differentiation as well.
I'm teaching a Pre-Calculus class but with students whose skill level is slightly below average (and most of whom won't be on a Calculus track for senior year/college), and using this Alg. II unit for the Trigonometry lessons has been really helpful. It breaks it down for them and covers all of the basics/necessities without getting too "into the weeds" on the parts that I knew they would struggle more with.
This is a great bridge to my textbook that is a little high for the average student. My lower level classes, this is the perfect fit in not set up and work. The topic examples are on target for the standards as well.
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Trigonometry (Algebra 2 Curriculum - Unit 12) | All Things Algebra®
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Description
Due to the length of this Trigonometry Unit Bundle , it is divided into two parts with two unit tests. In addition to the unit tests, each part includes guided notes, homework assignments, quizzes, and study guides to cover the following topics:
Unit 12 Part I:
• Pythagorean Theorem
• Special Right Triangles
• Trigonometric Functions (sin, cos, tan, csc, sec, cot)
• Finding Side and Angle Measures
• Applications: Angle of Elevation and Depression
• Angles in Standard Position
• Converting between Degrees and Radians
• Coterminal and Reference Angles
• Trigonometric Functions in the Coordinate Plane
• The Unit Circle
• Law of Sines
• Law of Cosines
• Area of Triangles
• Applications of Law of Sines, Law of Cosines, and Area
Unit 12 Part II:
• Graphing Trigonometric Functions
• Trigonometric Identities
• Sum and Difference of Angle Identities
• Double-Angle and Half-Angle Identities
• Solving Trigonometric Equations
ADDITIONAL COMPONENTS INCLUDED:
(1) Links to Instructional Videos: Links to videos of each lesson in the unit are included. Videos were created by fellow teachers for their students using the guided notes and shared in March 2020 when schools closed with no notice. Please watch through first before sharing with your students. Many teachers still use these in emergency substitute situations. (2) Editable Assessments: Editable versions of each quiz and the unit test are included. PowerPoint is required to edit these files. Individual problems can be changed to create multiple versions of the assessment. The layout of the assessment itself is not editable. If your Equation Editor is incompatible with mine (I use MathType), simply delete my equation and insert your own.
(3) Google Slides Version of the PDF: The second page of the Video links document contains a link to a Google Slides version of the PDF. Each page is set to the background in Google Slides. There are no text boxes; this is the PDF in Google Slides. I am unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead!
This resource is included in the following bundle(s):
Algebra 2 Curriculum
More Algebra 2 Units:
Unit 1 – Equations and Inequalities
Unit 2 – Linear Functions and Systems
Unit 3 – Parent Functions and Transformations
Unit 4 – Solving Quadratics and Complex Numbers
Unit 5 – Polynomial Functions
Unit 6 – Radical Functions
Unit 7 – Exponential and Logarithmic Functions
Unit 8 – Rational Functions
Unit 9 – Conic Sections
Unit 10 – Sequences and Series
Unit 11 – Probability and Statistics
LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable , meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at [email protected].
COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.
© All Things Algebra (Gina Wilson), 2012-present
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Law of Sines Worksheet
Students will practice applying the law of sines to calculate side lengths and angle measurements. This worksheet includes word problems as well as challenging bonus problems.
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Other Details
This is a 5 part worksheet:
- Part I Model Problems
- Part II Practice Problems (1-6)
- Part III Practice (harder) & Word Problems (7 - 18)
- Part IV Challenge Problems
- Part V Answer Key
- Pictures of Law of Sines (triangles, formula and more..)
- Law of Sines and Cosines Worksheets
Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!
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2.1 The Rectangular Coordinate Systems and Graphs
x -intercept is ( 4 , 0 ) ; ( 4 , 0 ) ; y- intercept is ( 0 , 3 ) . ( 0 , 3 ) .
125 = 5 5 125 = 5 5
( − 5 , 5 2 ) ( − 5 , 5 2 )
2.2 Linear Equations in One Variable
x = −5 x = −5
x = −3 x = −3
x = 10 3 x = 10 3
x = 1 x = 1
x = − 7 17 . x = − 7 17 . Excluded values are x = − 1 2 x = − 1 2 and x = − 1 3 . x = − 1 3 .
x = 1 3 x = 1 3
m = − 2 3 m = − 2 3
y = 4 x −3 y = 4 x −3
x + 3 y = 2 x + 3 y = 2
Horizontal line: y = 2 y = 2
Parallel lines: equations are written in slope-intercept form.
y = 5 x + 3 y = 5 x + 3
2.3 Models and Applications
C = 2.5 x + 3 , 650 C = 2.5 x + 3 , 650
L = 37 L = 37 cm, W = 18 W = 18 cm
2.4 Complex Numbers
−24 = 0 + 2 i 6 −24 = 0 + 2 i 6
( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i ( 3 −4 i ) − ( 2 + 5 i ) = 1 −9 i
5 2 − i 5 2 − i
18 + i 18 + i
−3 −4 i −3 −4 i
2.5 Quadratic Equations
( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1 ( x − 6 ) ( x + 1 ) = 0 ; x = 6 , x = − 1
( x −7 ) ( x + 3 ) = 0 , ( x −7 ) ( x + 3 ) = 0 , x = 7 , x = 7 , x = −3. x = −3.
( x + 5 ) ( x −5 ) = 0 , ( x + 5 ) ( x −5 ) = 0 , x = −5 , x = −5 , x = 5. x = 5.
( 3 x + 2 ) ( 4 x + 1 ) = 0 , ( 3 x + 2 ) ( 4 x + 1 ) = 0 , x = − 2 3 , x = − 2 3 , x = − 1 4 x = − 1 4
x = 0 , x = −10 , x = −1 x = 0 , x = −10 , x = −1
x = 4 ± 5 x = 4 ± 5
x = 3 ± 22 x = 3 ± 22
x = − 2 3 , x = − 2 3 , x = 1 3 x = 1 3
2.6 Other Types of Equations
{ −1 } { −1 }
0 , 0 , 1 2 , 1 2 , − 1 2 − 1 2
1 ; 1 ; extraneous solution − 2 9 − 2 9
−2 ; −2 ; extraneous solution −1 −1
−1 , −1 , 3 2 3 2
−3 , 3 , − i , i −3 , 3 , − i , i
2 , 12 2 , 12
−1 , −1 , 0 0 is not a solution.
2.7 Linear Inequalities and Absolute Value Inequalities
[ −3 , 5 ] [ −3 , 5 ]
( − ∞ , −2 ) ∪ [ 3 , ∞ ) ( − ∞ , −2 ) ∪ [ 3 , ∞ )
x < 1 x < 1
x ≥ −5 x ≥ −5
( 2 , ∞ ) ( 2 , ∞ )
[ − 3 14 , ∞ ) [ − 3 14 , ∞ )
6 < x ≤ 9 or ( 6 , 9 ] 6 < x ≤ 9 or ( 6 , 9 ]
( − 1 8 , 1 2 ) ( − 1 8 , 1 2 )
| x −2 | ≤ 3 | x −2 | ≤ 3
k ≤ 1 k ≤ 1 or k ≥ 7 ; k ≥ 7 ; in interval notation, this would be ( − ∞ , 1 ] ∪ [ 7 , ∞ ) . ( − ∞ , 1 ] ∪ [ 7 , ∞ ) .
2.1 Section Exercises
Answers may vary. Yes. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants.
The y -intercept is the point where the graph crosses the y -axis.
The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , 6 ) . ( 0 , 6 ) .
The x- intercept is ( 2 , 0 ) ( 2 , 0 ) and the y -intercept is ( 0 , −3 ) . ( 0 , −3 ) .
The x- intercept is ( 3 , 0 ) ( 3 , 0 ) and the y -intercept is ( 0 , 9 8 ) . ( 0 , 9 8 ) .
y = 4 − 2 x y = 4 − 2 x
y = 5 − 2 x 3 y = 5 − 2 x 3
y = 2 x − 4 5 y = 2 x − 4 5
d = 74 d = 74
d = 36 = 6 d = 36 = 6
d ≈ 62.97 d ≈ 62.97
( 3 , − 3 2 ) ( 3 , − 3 2 )
( 2 , −1 ) ( 2 , −1 )
( 0 , 0 ) ( 0 , 0 )
y = 0 y = 0
not collinear
A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 ) A: ( −3 , 2 ) , B: ( 1 , 3 ) , C: ( 4 , 0 )
d = 8.246 d = 8.246
d = 5 d = 5
( −3 , 4 ) ( −3 , 4 )
x = 0 y = −2 x = 0 y = −2
x = 0.75 y = 0 x = 0.75 y = 0
x = − 1.667 y = 0 x = − 1.667 y = 0
15 − 11.2 = 3.8 mi 15 − 11.2 = 3.8 mi shorter
6 .0 42 6 .0 42
Midpoint of each diagonal is the same point ( 2 , –2 ) ( 2 , –2 ) . Note this is a characteristic of rectangles, but not other quadrilaterals.
2.2 Section Exercises
It means they have the same slope.
The exponent of the x x variable is 1. It is called a first-degree equation.
If we insert either value into the equation, they make an expression in the equation undefined (zero in the denominator).
x = 2 x = 2
x = 2 7 x = 2 7
x = 6 x = 6
x = 3 x = 3
x = −14 x = −14
x ≠ −4 ; x ≠ −4 ; x = −3 x = −3
x ≠ 1 ; x ≠ 1 ; when we solve this we get x = 1 , x = 1 , which is excluded, therefore NO solution
x ≠ 0 ; x ≠ 0 ; x = − 5 2 x = − 5 2
y = − 4 5 x + 14 5 y = − 4 5 x + 14 5
y = − 3 4 x + 2 y = − 3 4 x + 2
y = 1 2 x + 5 2 y = 1 2 x + 5 2
y = −3 x − 5 y = −3 x − 5
y = 7 y = 7
y = −4 y = −4
8 x + 5 y = 7 8 x + 5 y = 7
Perpendicular
m = − 9 7 m = − 9 7
m = 3 2 m = 3 2
m 1 = − 1 3 , m 2 = 3 ; Perpendicular . m 1 = − 1 3 , m 2 = 3 ; Perpendicular .
y = 0.245 x − 45.662. y = 0.245 x − 45.662. Answers may vary. y min = −50 , y max = −40 y min = −50 , y max = −40
y = − 2.333 x + 6.667. y = − 2.333 x + 6.667. Answers may vary. y min = −10 , y max = 10 y min = −10 , y max = 10
y = − A B x + C B y = − A B x + C B
The slope for ( −1 , 1 ) to ( 0 , 4 ) is 3. The slope for ( −1 , 1 ) to ( 2 , 0 ) is − 1 3 . The slope for ( 2 , 0 ) to ( 3 , 3 ) is 3. The slope for ( 0 , 4 ) to ( 3 , 3 ) is − 1 3 . The slope for ( −1 , 1 ) to ( 0 , 4 ) is 3. The slope for ( −1 , 1 ) to ( 2 , 0 ) is − 1 3 . The slope for ( 2 , 0 ) to ( 3 , 3 ) is 3. The slope for ( 0 , 4 ) to ( 3 , 3 ) is − 1 3 .
Yes they are perpendicular.
2.3 Section Exercises
Answers may vary. Possible answers: We should define in words what our variable is representing. We should declare the variable. A heading.
2 , 000 − x 2 , 000 − x
v + 10 v + 10
Ann: 23 ; 23 ; Beth: 46 46
20 + 0.05 m 20 + 0.05 m
90 + 40 P 90 + 40 P
50 , 000 − x 50 , 000 − x
She traveled for 2 h at 20 mi/h, or 40 miles.
$5,000 at 8% and $15,000 at 12%
B = 100 + .05 x B = 100 + .05 x
R = 9 R = 9
r = 4 5 r = 4 5 or 0.8
W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14 W = P − 2 L 2 = 58 − 2 ( 15 ) 2 = 14
f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21 f = p q p + q = 8 ( 13 ) 8 + 13 = 104 21
m = − 5 4 m = − 5 4
h = 2 A b 1 + b 2 h = 2 A b 1 + b 2
length = 360 ft; width = 160 ft
A = 88 in . 2 A = 88 in . 2
h = V π r 2 h = V π r 2
r = V π h r = V π h
C = 12 π C = 12 π
2.4 Section Exercises
Add the real parts together and the imaginary parts together.
Possible answer: i i times i i equals -1, which is not imaginary.
−8 + 2 i −8 + 2 i
14 + 7 i 14 + 7 i
− 23 29 + 15 29 i − 23 29 + 15 29 i
8 − i 8 − i
−11 + 4 i −11 + 4 i
2 −5 i 2 −5 i
6 + 15 i 6 + 15 i
−16 + 32 i −16 + 32 i
−4 −7 i −4 −7 i
2 − 2 3 i 2 − 2 3 i
4 − 6 i 4 − 6 i
2 5 + 11 5 i 2 5 + 11 5 i
1 + i 3 1 + i 3
( 3 2 + 1 2 i ) 6 = −1 ( 3 2 + 1 2 i ) 6 = −1
5 −5 i 5 −5 i
9 2 − 9 2 i 9 2 − 9 2 i
2.5 Section Exercises
It is a second-degree equation (the highest variable exponent is 2).
We want to take advantage of the zero property of multiplication in the fact that if a ⋅ b = 0 a ⋅ b = 0 then it must follow that each factor separately offers a solution to the product being zero: a = 0 o r b = 0. a = 0 o r b = 0.
One, when no linear term is present (no x term), such as x 2 = 16. x 2 = 16. Two, when the equation is already in the form ( a x + b ) 2 = d . ( a x + b ) 2 = d .
x = 6 , x = 6 , x = 3 x = 3
x = − 5 2 , x = − 5 2 , x = − 1 3 x = − 1 3
x = 5 , x = 5 , x = −5 x = −5
x = − 3 2 , x = − 3 2 , x = 3 2 x = 3 2
x = −2 , 3 x = −2 , 3
x = 0 , x = 0 , x = − 3 7 x = − 3 7
x = −6 , x = −6 , x = 6 x = 6
x = 6 , x = 6 , x = −4 x = −4
x = 1 , x = 1 , x = −2 x = −2
x = −2 , x = −2 , x = 11 x = 11
z = 2 3 , z = 2 3 , z = − 1 2 z = − 1 2
x = 3 ± 17 4 x = 3 ± 17 4
One rational
Two real; rational
x = − 1 ± 17 2 x = − 1 ± 17 2
x = 5 ± 13 6 x = 5 ± 13 6
x = − 1 ± 17 8 x = − 1 ± 17 8
x ≈ 0.131 x ≈ 0.131 and x ≈ 2.535 x ≈ 2.535
x ≈ − 6.7 x ≈ − 6.7 and x ≈ 1.7 x ≈ 1.7
a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a a x 2 + b x + c = 0 x 2 + b a x = − c a x 2 + b a x + b 2 4 a 2 = − c a + b 4 a 2 ( x + b 2 a ) 2 = b 2 − 4 a c 4 a 2 x + b 2 a = ± b 2 − 4 a c 4 a 2 x = − b ± b 2 − 4 a c 2 a
x ( x + 10 ) = 119 ; x ( x + 10 ) = 119 ; 7 ft. and 17 ft.
maximum at x = 70 x = 70
The quadratic equation would be ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. ( 100 x −0.5 x 2 ) − ( 60 x + 300 ) = 300. The two values of x x are 20 and 60.
2.6 Section Exercises
This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.
He or she is probably trying to enter negative 9, but taking the square root of −9 −9 is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in −27. −27.
A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.
x = 81 x = 81
x = 17 x = 17
x = 8 , x = 27 x = 8 , x = 27
x = −2 , 1 , −1 x = −2 , 1 , −1
y = 0 , 3 2 , − 3 2 y = 0 , 3 2 , − 3 2
m = 1 , −1 m = 1 , −1
x = 2 5 , ±3 i x = 2 5 , ±3 i
x = 32 x = 32
t = 44 3 t = 44 3
x = −2 x = −2
x = 4 , −4 3 x = 4 , −4 3
x = − 5 4 , 7 4 x = − 5 4 , 7 4
x = 3 , −2 x = 3 , −2
x = 1 , −1 , 3 , -3 x = 1 , −1 , 3 , -3
x = 2 , −2 x = 2 , −2
x = 1 , 5 x = 1 , 5
x ≥ 0 x ≥ 0
x = 4 , 6 , −6 , −8 x = 4 , 6 , −6 , −8
2.7 Section Exercises
When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.
( − ∞ , ∞ ) ( − ∞ , ∞ )
We start by finding the x -intercept, or where the function = 0. Once we have that point, which is ( 3 , 0 ) , ( 3 , 0 ) , we graph to the right the straight line graph y = x −3 , y = x −3 , and then when we draw it to the left we plot positive y values, taking the absolute value of them.
( − ∞ , 3 4 ] ( − ∞ , 3 4 ]
[ − 13 2 , ∞ ) [ − 13 2 , ∞ )
( − ∞ , 3 ) ( − ∞ , 3 )
( − ∞ , − 37 3 ] ( − ∞ , − 37 3 ]
All real numbers ( − ∞ , ∞ ) ( − ∞ , ∞ )
( − ∞ , − 10 3 ) ∪ ( 4 , ∞ ) ( − ∞ , − 10 3 ) ∪ ( 4 , ∞ )
( − ∞ , −4 ] ∪ [ 8 , + ∞ ) ( − ∞ , −4 ] ∪ [ 8 , + ∞ )
No solution
( −5 , 11 ) ( −5 , 11 )
[ 6 , 12 ] [ 6 , 12 ]
[ −10 , 12 ] [ −10 , 12 ]
x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 , ( − 2 , + ∞ ) x > − 6 and x > − 2 Take the intersection of two sets . x > − 2 , ( − 2 , + ∞ )
x < − 3 or x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ [ 1 , ∞ ) x < − 3 or x ≥ 1 Take the union of the two sets . ( − ∞ , − 3 ) ∪ [ 1 , ∞ )
( − ∞ , −1 ) ∪ ( 3 , ∞ ) ( − ∞ , −1 ) ∪ ( 3 , ∞ )
[ −11 , −3 ] [ −11 , −3 ]
It is never less than zero. No solution.
Where the blue line is above the orange line; point of intersection is x = − 3. x = − 3.
( − ∞ , −3 ) ( − ∞ , −3 )
Where the blue line is above the orange line; always. All real numbers.
( − ∞ , − ∞ ) ( − ∞ , − ∞ )
( −1 , 3 ) ( −1 , 3 )
( − ∞ , 4 ) ( − ∞ , 4 )
{ x | x < 6 } { x | x < 6 }
{ x | −3 ≤ x < 5 } { x | −3 ≤ x < 5 }
( −2 , 1 ] ( −2 , 1 ]
( − ∞ , 4 ] ( − ∞ , 4 ]
Where the blue is below the orange; always. All real numbers. ( − ∞ , + ∞ ) . ( − ∞ , + ∞ ) .
Where the blue is below the orange; ( 1 , 7 ) . ( 1 , 7 ) .
x = 2 , − 4 5 x = 2 , − 4 5
( −7 , 5 ] ( −7 , 5 ]
80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400 80 ≤ T ≤ 120 1 , 600 ≤ 20 T ≤ 2 , 400
[ 1 , 600 , 2 , 400 ] [ 1 , 600 , 2 , 400 ]
Review Exercises
x -intercept: ( 3 , 0 ) ; ( 3 , 0 ) ; y -intercept: ( 0 , −4 ) ( 0 , −4 )
y = 5 3 x + 4 y = 5 3 x + 4
72 = 6 2 72 = 6 2
620.097 620.097
midpoint is ( 2 , 23 2 ) ( 2 , 23 2 )
x = 4 x = 4
x = 12 7 x = 12 7
y = 1 6 x + 4 3 y = 1 6 x + 4 3
y = 2 3 x + 6 y = 2 3 x + 6
females 17, males 56
x = − 3 4 ± i 47 4 x = − 3 4 ± i 47 4
horizontal component −2 ; −2 ; vertical component −1 −1
7 + 11 i 7 + 11 i
−16 − 30 i −16 − 30 i
−4 − i 10 −4 − i 10
x = 7 − 3 i x = 7 − 3 i
x = −1 , −5 x = −1 , −5
x = 0 , 9 7 x = 0 , 9 7
x = 10 , −2 x = 10 , −2
x = − 1 ± 5 4 x = − 1 ± 5 4
x = 2 5 , − 1 3 x = 2 5 , − 1 3
x = 5 ± 2 7 x = 5 ± 2 7
x = 0 , 256 x = 0 , 256
x = 0 , ± 2 x = 0 , ± 2
x = 11 2 , −17 2 x = 11 2 , −17 2
[ − 10 3 , 2 ] [ − 10 3 , 2 ]
( − 4 3 , 1 5 ) ( − 4 3 , 1 5 )
Where the blue is below the orange line; point of intersection is x = 3.5. x = 3.5.
( 3.5 , ∞ ) ( 3.5 , ∞ )
Practice Test
y = 3 2 x + 2 y = 3 2 x + 2
( 0 , −3 ) ( 0 , −3 ) ( 4 , 0 ) ( 4 , 0 )
( − ∞ , 9 ] ( − ∞ , 9 ]
x = −15 x = −15
x ≠ −4 , 2 ; x ≠ −4 , 2 ; x = − 5 2 , 1 x = − 5 2 , 1
x = 3 ± 3 2 x = 3 ± 3 2
( −4 , 1 ) ( −4 , 1 )
y = −5 9 x − 2 9 y = −5 9 x − 2 9
y = 5 2 x − 4 y = 5 2 x − 4
5 13 − 14 13 i 5 13 − 14 13 i
x = 2 , − 4 3 x = 2 , − 4 3
x = 1 2 ± 2 2 x = 1 2 ± 2 2
x = 1 2 , 2 , −2 x = 1 2 , 2 , −2
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Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites
- Authors: Jay Abramson
- Publisher/website: OpenStax
- Book title: Algebra and Trigonometry
- Publication date: Feb 13, 2015
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites
- Section URL: https://openstax.org/books/algebra-and-trigonometry/pages/chapter-2
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Step 1. Name: Date: Unit 12: Trigonometry Bell: Homework 2: Finding Side and Angle Mease ** This is a 2-page document! ** Directions: Find each missing measure. Round all answers to the nearest tenth.
There are two different ways you can leave this answer! In the notes, leave itin terms ofsin2Ð. In the homework, you will be 9/'verifying" and leaving it in terms ofcos2Ð c. sin2Ð — 2 sine + 1 I —l CO )(sinÐ + COS 9) a. (sine
12.3_notes_evaluating_trig.pdf. File Size: 322 kb. File Type: pdf. Download File. Homework Solutions. Homework Solutions will now be posted after the homework has been stamped or collected. Please try the problems on your own and ask questions in class!
At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Trigonometry 12th Edition, you'll learn how to solve your toughest homework problems. Our resource for Trigonometry includes answers to chapter exercises, as ...
Find an answer to your question Trigonometry unit 12, homework 2: finding side and angle measures Find each missing measure. Round all answers to the nearest…
At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Trigonometry 11th Edition, you'll learn how to solve your toughest homework problems. Our resource for Trigonometry includes answers to chapter exercises, as well as detailed information to walk you through ...
Translating Trigonometric Graphs: Phase/Vertical Shifts *with sine, cosine, and tangent graphs only* HW #10
This unit includes 96 pages of guided notes, homework assignments, three quizzes, two study guides, and two unit tests that cover the topics listed in the description below.
Study with Quizlet and memorize flashcards containing terms like trigonometric ratios, oblique, law of cosines and more.
Assessment. Unit 12 Mid-Unit Quiz (Through Lesson 4) - Form C. ASSESSMENT. ANSWER KEY. EDITABLE ASSESSMENT. EDITABLE KEY.
Name: Date: Unit 8: Right Triangles & Trigonometry Homework 9: Law of Sines & Law of Cosines; + Applications This is a 2-page document! ** Directions: Use the Law of Sines and/or the Law of Cosines to solve each triangle.
Free Trignometry worksheets includes visual aides, model problems, exploratory activities, practice problems, and an online component
Due to the length of this Trigonometry Unit Bundle, it is divided into two parts with two unit tests. In addition to the unit tests, each part includes guided notes, homework assignments, quizzes, and study guides to cover the following topics:Unit 12 Part I:• Pythagorean Theorem• Special Right Tri...
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Unit 12 - Statistics. The field of statistics is rich with details and theory that cannot even begin to be touched in this unit. A true study of statistics and the interpretation and comparison of data sets truly needs deeper treatment than what is given in this time-limited course. This unit begins by introducing sigma notation.
Other Math questions and answers. Name: Date: Unit 12: Trigonometry Bell: — Homework 3: Angles and Angle Measure ** This is a 2-page document ** Directions: Convert each measure to radians. 1. 225 2. 20 3.-255 4.-140" 5. 75 6.-300 Directions: Convert each measure to degrees. 7.7 831- 12. Directions: Sketch each angle.
report flag outlined. Answer: Step-by-step explanation: just a plain answer it's B. arrow right. Explore similar answers. messages. Get this answer verified by an Expert.
Unit 12: trigonometry, homework 3: angles and angle measure Get the answers you need, now!