Question 1

Simplify the expression algebraically.​ $$3 \cos ( \pi - \theta ) + 3 \sin \left( \frac { \pi } { 2 } + \theta \right)$$ ​

Accepted Answer

A)  $3 \cos ( \theta ) - 3 \sin ( \theta )$ 
B) 0 
C)  $3 \cos ( \theta ) + 3 \sin ( \theta )$ 
D) 1 
E) 6 
A)  $3 \cos ( \theta ) - 3 \sin ( \theta )$ 
B) 0 
C)  $3 \cos ( \theta ) + 3 \sin ( \theta )$ 
D) 1 
E) 6 B

Question 2

A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system,the weight moves vertically from its equilibrium position,and this motion is modeled by​ $y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$ ​ where y is the distance from equilibrium (in feet)and t is the time (in seconds).
​
Use the identity $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ where $C = \arctan ( b / a ) , a > 0$ ,to write the model in the form $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B t + C )$ .
​

Accepted Answer

A)  $y = \sin ( 2 t + 0.9273 )$ 
B)  $y = \frac { 24 } { 5 } \sin ( 2 t + 0.9273 )$ ​ 
C)  $y = \frac { 24 } { 5 } \sin ( 2 t - 0.9273 )$ 
D)  $y = \sin ( 2 t - 0.9273 )$ 
E)  $y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )$ 
A)  $y = \sin ( 2 t + 0.9273 )$ 
B)  $y = \frac { 24 } { 5 } \sin ( 2 t + 0.9273 )$ ​ 
C)  $y = \frac { 24 } { 5 } \sin ( 2 t - 0.9273 )$ 
D)  $y = \sin ( 2 t - 0.9273 )$ 
E)  $y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )$ E

Question 3

Find the exact value of the given expression using a sum or difference formula. $$\sin 285 ^ { \circ }$$

Accepted Answer

A)  $\frac { ( \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
B)  $\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
C)  $\frac { ( \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
D)  $\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
A)  $\frac { ( \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
B)  $\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
C)  $\frac { ( \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
D)  $\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ B

Question 4

Find the exact value of the given expression using a sum or difference formula. $$\cos \frac { 17 \pi } { 12 }$$

Accepted Answer

A)  $\frac { ( \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
B)  $\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
C)  $\frac { ( \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
D)  $\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
A)  $\frac { ( \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
B)  $\frac { ( - \sqrt { 3 } + 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
C)  $\frac { ( \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$ 
D)  $\frac { ( - \sqrt { 3 } - 1 ) ( 2 \sqrt { 2 } ) } { 8 }$

Question 5

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 7 } { 25 }$ and $\cos v = - \frac { 12 } { 13 }$ .(Both u and v are in Quadrant II. )

Accepted Answer

A)  $\sin ( u + v ) = \frac { 36 } { 325 }$ 
B)  $\sin ( u + v ) = - \frac { 36 } { 325 }$ 
C)  $\sin ( u + v ) = - \frac { 204 } { 325 }$ 
D)  $\sin ( u + v ) = - \frac { 253 } { 325 }$ 
E)  $\sin ( u + v ) = \frac { 204 } { 325 }$ 
A)  $\sin ( u + v ) = \frac { 36 } { 325 }$ 
B)  $\sin ( u + v ) = - \frac { 36 } { 325 }$ 
C)  $\sin ( u + v ) = - \frac { 204 } { 325 }$ 
D)  $\sin ( u + v ) = - \frac { 253 } { 325 }$ 
E)  $\sin ( u + v ) = \frac { 204 } { 325 }$

Question 6

Simplify the given expression algebraically. $\cos \left( \frac { \pi } { 2 } + x \right)$

Accepted Answer

A)  $\cos x$ 
B)  $- \sin x$ 
C)  $\sin x$ 
D) 1 
E)  $- \cos x$ 
A)  $\cos x$ 
B)  $- \sin x$ 
C)  $\sin x$ 
D) 1 
E)  $- \cos x$

Question 7

Find the expression as the tangent of an angle.​ $$\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }$$ ​

Accepted Answer

A)  $\tan 2 x$ 
B)  $\tan 3 x$ 
C)  $\tan 4 x$ 
D)  $\tan ^ { - 1 } 4 x$ 
E)  $\tan ^ { - 1 } 2 x$ 
A)  $\tan 2 x$ 
B)  $\tan 3 x$ 
C)  $\tan 4 x$ 
D)  $\tan ^ { - 1 } 4 x$ 
E)  $\tan ^ { - 1 } 2 x$

Question 8

Use the formula $$a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$$ ,where $C = \arctan ( b / a ) , a = 3 , b = , B = 1$ to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

Accepted Answer

A)  $\sin ( \theta + 0.3218 )$ 
B)  $\sin ( \theta - 0.3218 )$ 
C) 3 $\sin ( \theta + 0.3218 )$ 
D)  $\sqrt { 10 }$ $\sin ( \theta - 0.3218 )$ 
E)  $\sqrt { 10 }$ $\sin ( \theta + 0.3218 )$ 
A)  $\sin ( \theta + 0.3218 )$ 
B)  $\sin ( \theta - 0.3218 )$ 
C) 3 $\sin ( \theta + 0.3218 )$ 
D)  $\sqrt { 10 }$ $\sin ( \theta - 0.3218 )$ 
E)  $\sqrt { 10 }$ $\sin ( \theta + 0.3218 )$

Question 9

Write the given expression as the sine of an angle. $$\sin 85 ^ { \circ } \cos 50 ^ { \circ } - \sin 50 ^ { \circ } \cos 85 ^ { \circ }$$

Accepted Answer

A)  $\sin \left( 135 ^ { \circ } \right)$ 
B)  $\sin \left( - 100 ^ { \circ } \right)$ 
C)  $\sin \left( 35 ^ { \circ } \right)$ 
D)  $\sin \left( 50 ^ { \circ } \right)$ 
E)  $\sin \left( 85 ^ { \circ } \right)$ 
A)  $\sin \left( 135 ^ { \circ } \right)$ 
B)  $\sin \left( - 100 ^ { \circ } \right)$ 
C)  $\sin \left( 35 ^ { \circ } \right)$ 
D)  $\sin \left( 50 ^ { \circ } \right)$ 
E)  $\sin \left( 85 ^ { \circ } \right)$

Question 10

Find the exact solutions of the given equation in the interval $[ 0,2 \pi )$ . sin 4x= -2sin 2x

Accepted Answer

A)  $x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
B)  $x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 }$ 
C)  $x = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }$ 
D)  $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$ 
E)  $x = \frac { 7 \pi } { 6 } , \frac { 3 \pi } { 2 } , \frac { 11 \pi } { 6 }$ 
A)  $x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$ 
B)  $x = 0 , \frac { \pi } { 3 } , \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 }$ 
C)  $x = \frac { \pi } { 6 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 2 }$ 
D)  $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$ 
E)  $x = \frac { 7 \pi } { 6 } , \frac { 3 \pi } { 2 } , \frac { 11 \pi } { 6 }$

Question 11

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta - C )$ ,where $C = \arctan ( a / b ) , a = 2 , b = 8 , B = 1$ ,to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta - C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

Accepted Answer

A) 2 $\cos ( \theta + 0.245 )$ 
B)  $2 \sqrt { 17 }$ $\cos ( \theta - 0.245 )$ 
C)  $2 \sqrt { 17 }$ $\cos ( \theta + 0.245 )$ 
D) 2 $\cos ( \theta - 0.245 )$ 
E) 8 $\cos ( \theta - 0.245 )$ 
A) 2 $\cos ( \theta + 0.245 )$ 
B)  $2 \sqrt { 17 }$ $\cos ( \theta - 0.245 )$ 
C)  $2 \sqrt { 17 }$ $\cos ( \theta + 0.245 )$ 
D) 2 $\cos ( \theta - 0.245 )$ 
E) 8 $\cos ( \theta - 0.245 )$

Question 12

Write the given expression as the tangent of an angle.​ $$\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }$$

Accepted Answer

A)  $\tan ( - 17 x )$ 
B)  $\tan ( 11 x )$ 
C)  $\tan ( 7 x )$ 
D)  $\tan ( 3 x )$ 
E)  $\tan ( 5 x )$ 
A)  $\tan ( - 17 x )$ 
B)  $\tan ( 11 x )$ 
C)  $\tan ( 7 x )$ 
D)  $\tan ( 3 x )$ 
E)  $\tan ( 5 x )$

Question 13

Find the exact value of $\cos ( u + v )$ given that $\sin u = \frac { 8 } { 17 }$ and $\cos v = - \frac { 60 } { 61 }$ .(Both u and v are in Quadrant II. )

Accepted Answer

A)  $\cos ( u + v ) = \frac { 812 } { 1037 }$ 
B)  $\cos ( u + v ) = - \frac { 300 } { 1037 }$ 
C)  $\cos ( u + v ) = - \frac { 804 } { 1037 }$ 
D)  $\cos ( u + v ) = \frac { 315 } { 1037 }$ 
E)  $\cos ( u + v ) = \frac { 645 } { 1037 }$ 
A)  $\cos ( u + v ) = \frac { 812 } { 1037 }$ 
B)  $\cos ( u + v ) = - \frac { 300 } { 1037 }$ 
C)  $\cos ( u + v ) = - \frac { 804 } { 1037 }$ 
D)  $\cos ( u + v ) = \frac { 315 } { 1037 }$ 
E)  $\cos ( u + v ) = \frac { 645 } { 1037 }$

Question 14

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b ) , a > 0$ ,to rewrite the trigonometric expression in the form.​ $\sqrt { 6 } \sin \left( \theta + \frac { \pi } { 4 } \right)$ ​

Accepted Answer

A)  $$\sqrt { 3 } \sin \theta - \sqrt { 3 } \cos \theta$$ 
B)  $$\sqrt { 3 } \sin \theta + \cos \theta$$ 
C)  $\sin \theta - \sqrt { 3 } \cos \theta$ 
D)  $\sqrt { 3 } \sin \theta + \sqrt { 3 } \cos \theta$ 
E)  $\sin \theta + \cos \theta$ 
A)  $$\sqrt { 3 } \sin \theta - \sqrt { 3 } \cos \theta$$ 
B)  $$\sqrt { 3 } \sin \theta + \cos \theta$$ 
C)  $\sin \theta - \sqrt { 3 } \cos \theta$ 
D)  $\sqrt { 3 } \sin \theta + \sqrt { 3 } \cos \theta$ 
E)  $\sin \theta + \cos \theta$

Question 15

Find the expression as the tangent of an angle.​ $$\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }$$ ​

Accepted Answer

A)  $\tan 40 ^ { \circ }$ 
B)  $\tan 60 ^ { \circ }$ 
C)  $\tan ^ { - 1 } 80 ^ { \circ }$ 
D)  $\tan 20 ^ { \circ }$ 
E)  $\tan ^ { - 1 } 40 ^ { \circ }$ 
A)  $\tan 40 ^ { \circ }$ 
B)  $\tan 60 ^ { \circ }$ 
C)  $\tan ^ { - 1 } 80 ^ { \circ }$ 
D)  $\tan 20 ^ { \circ }$ 
E)  $\tan ^ { - 1 } 40 ^ { \circ }$

Question 16

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ,where $C = \arctan ( b / a ) , a = 18 , b = 6 , B = 3$ ,to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

Accepted Answer

A)  $6 \sqrt { 10 }$ $\sin ( \theta - 0.3218 )$ 
B)  $6 \sqrt { 10 }$ $\sin ( 3 \theta + 0.3218 )$ 
C)  $\sin ( 3 \theta + 0.3218 )$ 
D)  $6 \sqrt { 10 }$ $\sin ( 3 \theta - 0.3218 )$ 
E)  $6 \sqrt { 10 }$ $\sin ( \theta + 0.3218 )$ 
A)  $6 \sqrt { 10 }$ $\sin ( \theta - 0.3218 )$ 
B)  $6 \sqrt { 10 }$ $\sin ( 3 \theta + 0.3218 )$ 
C)  $\sin ( 3 \theta + 0.3218 )$ 
D)  $6 \sqrt { 10 }$ $\sin ( 3 \theta - 0.3218 )$ 
E)  $6 \sqrt { 10 }$ $\sin ( \theta + 0.3218 )$

Question 17

Find the expression as the sine of an angle.​ $$\sin 55 ^ { \circ } \cos 5 ^ { \circ } + \cos 55 ^ { \circ } \sin 5 ^ { \circ }$$ ​

Accepted Answer

A)  $\sin 55 ^ { \circ }$ 
B)  $\cos 60 ^ { \circ }$ 
C)  $\cos 50 ^ { \circ }$ 
D)  $\sin 60 ^ { \circ }$ 
E)  $\sin 50 ^ { \circ }$ 
A)  $\sin 55 ^ { \circ }$ 
B)  $\cos 60 ^ { \circ }$ 
C)  $\cos 50 ^ { \circ }$ 
D)  $\sin 60 ^ { \circ }$ 
E)  $\sin 50 ^ { \circ }$

Question 18

Simplify the expression algebraically.​ $$\sin ( 9 x + 9 y ) \sin ( 9 x - 9 y )$$ ​

Accepted Answer

A)  $\sin ^ { 2 } x - \sin ^ { 2 } 9 y$ 
B)  $\sin ^ { 2 } 9 x + \sin ^ { 2 } 9 y$ 
C)  $\sin ^ { 2 } 9 x - \sin ^ { 2 } 9 y$ 
D)  $\sin ^ { 2 } x + \sin ^ { 2 } y$ 
E)  $\sin ^ { 2 } 9 x - \sin ^ { 2 } y$ 
A)  $\sin ^ { 2 } x - \sin ^ { 2 } 9 y$ 
B)  $\sin ^ { 2 } 9 x + \sin ^ { 2 } 9 y$ 
C)  $\sin ^ { 2 } 9 x - \sin ^ { 2 } 9 y$ 
D)  $\sin ^ { 2 } x + \sin ^ { 2 } y$ 
E)  $\sin ^ { 2 } 9 x - \sin ^ { 2 } y$

Question 19

Evaluate the expression.​ $\sin x \sin ( x + y ) + \cos x \cos ( x + y )$ ​

Accepted Answer

A)  $\sin ^ { 2 } x - \sin ^ { 2 } y$ 
B) 0 
C)  $\sin x \cos x + \sin y \cos y$ 
D)  $\cos y$ 
E)  $\cos ^ { 2 } x - \sin ^ { 2 } x$ 
A)  $\sin ^ { 2 } x - \sin ^ { 2 } y$ 
B) 0 
C)  $\sin x \cos x + \sin y \cos y$ 
D)  $\cos y$ 
E)  $\cos ^ { 2 } x - \sin ^ { 2 } x$

Question 20

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ,where $C = \arctan ( b / a ) , a = 1 , b = 3 , B = 2$ ,to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

Accepted Answer

A)  $\sqrt { 10 }$ $\sin ( 2 \theta + 1.249 )$ 
B)  $\sqrt { 10 }$ $\sin ( \theta - 1.249 )$ 
C)  $\sqrt { 10 }$ $\sin ( 2 \theta - 1.249 )$ 
D)  $\sqrt { 10 }$ $\sin ( \theta + 1.249 )$ 
E)  $\sin ( 2 \theta + 1.249 )$ 
A)  $\sqrt { 10 }$ $\sin ( 2 \theta + 1.249 )$ 
B)  $\sqrt { 10 }$ $\sin ( \theta - 1.249 )$ 
C)  $\sqrt { 10 }$ $\sin ( 2 \theta - 1.249 )$ 
D)  $\sqrt { 10 }$ $\sin ( \theta + 1.249 )$ 
E)  $\sin ( 2 \theta + 1.249 )$

Exam 34: Sum and Difference Formulas

Simplify the expression algebraically.​ 3cos⁡(π−θ)+3sin⁡(π2+θ)3 \cos ( \pi - \theta ) + 3 \sin \left( \frac { \pi } { 2 } + \theta \right)3cos(π−θ)+3sin(2π​+θ) ​

Find the exact value of the given expression using a sum or difference formula. sin⁡285∘\sin 285 ^ { \circ }sin285∘

Find the exact value of the given expression using a sum or difference formula. cos⁡17π12\cos \frac { 17 \pi } { 12 }cos1217π​

Find the exact value of sin⁡(u+v)\sin ( u + v )sin(u+v) given that sin⁡u=725\sin u = \frac { 7 } { 25 }sinu=257​ and cos⁡v=−1213\cos v = - \frac { 12 } { 13 }cosv=−1312​ .(Both u and v are in Quadrant II. )

Simplify the given expression algebraically. cos⁡(π2+x)\cos \left( \frac { \pi } { 2 } + x \right)cos(2π​+x)

Find the expression as the tangent of an angle.​ tan⁡3x+tan⁡x1−tan⁡3xtan⁡x\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }1−tan3xtanxtan3x+tanx​ ​

Write the given expression as the sine of an angle. sin⁡85∘cos⁡50∘−sin⁡50∘cos⁡85∘\sin 85 ^ { \circ } \cos 50 ^ { \circ } - \sin 50 ^ { \circ } \cos 85 ^ { \circ }sin85∘cos50∘−sin50∘cos85∘

Find the exact solutions of the given equation in the interval [0,2π)[ 0,2 \pi )[0,2π) . sin 4x= -2sin 2x

Write the given expression as the tangent of an angle.​ tan⁡7x+tan⁡4x1−tan⁡7xtan⁡4x\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }1−tan7xtan4xtan7x+tan4x​

Find the exact value of cos⁡(u+v)\cos ( u + v )cos(u+v) given that sin⁡u=817\sin u = \frac { 8 } { 17 }sinu=178​ and cos⁡v=−6061\cos v = - \frac { 60 } { 61 }cosv=−6160​ .(Both u and v are in Quadrant II. )

Find the expression as the tangent of an angle.​ tan⁡60∘−tan⁡20∘1+tan⁡60∘tan⁡20∘\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }1+tan60∘tan20∘tan60∘−tan20∘​ ​

Find the expression as the sine of an angle.​ sin⁡55∘cos⁡5∘+cos⁡55∘sin⁡5∘\sin 55 ^ { \circ } \cos 5 ^ { \circ } + \cos 55 ^ { \circ } \sin 5 ^ { \circ }sin55∘cos5∘+cos55∘sin5∘ ​

Simplify the expression algebraically.​ sin⁡(9x+9y)sin⁡(9x−9y)\sin ( 9 x + 9 y ) \sin ( 9 x - 9 y )sin(9x+9y)sin(9x−9y) ​

Evaluate the expression.​ sin⁡xsin⁡(x+y)+cos⁡xcos⁡(x+y)\sin x \sin ( x + y ) + \cos x \cos ( x + y )sinxsin(x+y)+cosxcos(x+y) ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Simplify the expression algebraically. $3 \cos ( \pi - \theta ) + 3 \sin \left( \frac { \pi } { 2 } + \theta \right)$

Find the exact value of the given expression using a sum or difference formula. $\sin 285 ^ { \circ }$

Find the exact value of the given expression using a sum or difference formula. $\cos \frac { 17 \pi } { 12 }$

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 7 } { 25 }$ and $\cos v = - \frac { 12 } { 13 }$ .(Both u and v are in Quadrant II. )

Simplify the given expression algebraically. $\cos \left( \frac { \pi } { 2 } + x \right)$

Find the expression as the tangent of an angle. $\frac { \tan 3 x + \tan x } { 1 - \tan 3 x \tan x }$

Write the given expression as the sine of an angle. $\sin 85 ^ { \circ } \cos 50 ^ { \circ } - \sin 50 ^ { \circ } \cos 85 ^ { \circ }$

Find the exact solutions of the given equation in the interval $[ 0,2 \pi )$ . sin 4x= -2sin 2x

Write the given expression as the tangent of an angle. $\frac { \tan 7 x + \tan 4 x } { 1 - \tan 7 x \tan 4 x }$

Find the exact value of $\cos ( u + v )$ given that $\sin u = \frac { 8 } { 17 }$ and $\cos v = - \frac { 60 } { 61 }$ .(Both u and v are in Quadrant II. )

Find the expression as the tangent of an angle. $\frac { \tan 60 ^ { \circ } - \tan 20 ^ { \circ } } { 1 + \tan 60 ^ { \circ } \tan 20 ^ { \circ } }$

Find the expression as the sine of an angle. $\sin 55 ^ { \circ } \cos 5 ^ { \circ } + \cos 55 ^ { \circ } \sin 5 ^ { \circ }$

Simplify the expression algebraically. $\sin ( 9 x + 9 y ) \sin ( 9 x - 9 y )$

Evaluate the expression. $\sin x \sin ( x + y ) + \cos x \cos ( x + y )$