Question 1

Which of the following is a solution to the given equation?  
Cscx - 2 = 0

Accepted Answer

A)   $x = \frac { 2 \pi } { 3 }$ 
B)   $x = \frac { \pi } { 4 }$ 
C)   $x = \frac { \pi } { 4 }$. 
D)   $x = \frac { \pi } { 6 }$ 
E)   $x = \frac { 7 \pi } { 4 }$ 
A)   $x = \frac { 2 \pi } { 3 }$ 
B)   $x = \frac { \pi } { 4 }$ 
C)   $x = \frac { \pi } { 4 }$. 
D)   $x = \frac { \pi } { 6 }$ 
E)   $x = \frac { 7 \pi } { 4 }$

Question 2

Solve the following equation.   $\sin x ( 5 \sin x + 5 ) = 0$

Accepted Answer

A)   $n \pi , \frac { \pi } { 2 } + 2 n \pi$ 
B)   $\frac { 2 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
C)  $n \pi , \frac { 3 \pi } { 2 } + 2 n \pi$ 
D)   $\frac { \pi } { 3 } + n \pi , \frac { \pi } { 3 } + n \pi$ 
E)   $\pi , \frac { 5 \pi } { 2 } + 2 n \pi$ 
A)   $n \pi , \frac { \pi } { 2 } + 2 n \pi$ 
B)   $\frac { 2 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
C)  $n \pi , \frac { 3 \pi } { 2 } + 2 n \pi$ 
D)   $\frac { \pi } { 3 } + n \pi , \frac { \pi } { 3 } + n \pi$ 
E)   $\pi , \frac { 5 \pi } { 2 } + 2 n \pi$

Question 3

Find the exact value of the given expression using a sum or difference formula. $\cos \frac { 13 \pi } { 12 }$

Accepted Answer

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

Question 4

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ , where $C = \arctan ( a / b )$ $C = \arctan ( a / b ) , a > 0$ , to rewrite the trigonometric expression in the form $a \sin B \theta + b \cos B \theta$   9 $\cos \left( \theta - \frac { \pi } { 4 } \right)$

Accepted Answer

A)  $\frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
B)  $- \frac { 9 \sqrt { 2 } } { 2 } \sin \theta - \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
C)  $- \frac { 9 \sqrt { 2 } } { 2 } \sin \theta + \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
D)  $\frac { 9 \sqrt { 2 } } { 2 } \sin \theta + \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
E)  $\frac { 9 \sqrt { 2 } } { 2 } \sin \theta - \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
A)  $\frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
B)  $- \frac { 9 \sqrt { 2 } } { 2 } \sin \theta - \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
C)  $- \frac { 9 \sqrt { 2 } } { 2 } \sin \theta + \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
D)  $\frac { 9 \sqrt { 2 } } { 2 } \sin \theta + \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$ 
E)  $\frac { 9 \sqrt { 2 } } { 2 } \sin \theta - \frac { 9 \sqrt { 2 } } { 2 } \cos \theta$

Question 5

Which of the following expressions is equivalent to the given expression $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$ ? 
($\theta $  $\neq$ $\pi$n, where n is a whole number)

Accepted Answer

A)  $\frac { 1 - \cos \theta } { | \sin \theta | }$ 
B)  $\frac { 5 - 5 \cos \theta } { | \sin \theta | }$ 
C)  $\frac { 5 + 5 \sin \theta } { | \cos \theta | }$ 
D)  $\frac { 5 - 5 \sin \theta } { | \cos \theta | }$ 
E)  $\frac { 5 + 5 \cos \theta } { | \sin \theta | }$ 
A)  $\frac { 1 - \cos \theta } { | \sin \theta | }$ 
B)  $\frac { 5 - 5 \cos \theta } { | \sin \theta | }$ 
C)  $\frac { 5 + 5 \sin \theta } { | \cos \theta | }$ 
D)  $\frac { 5 - 5 \sin \theta } { | \cos \theta | }$ 
E)  $\frac { 5 + 5 \cos \theta } { | \sin \theta | }$

Question 6

Solve the multiple-angle equation. 
 $2 \sec 4 x = 4$

Accepted Answer

A)  $\frac { \pi } { 12 } - \frac { n \pi } { 3 } , \frac { 5 \pi } { 12 } + \frac { n \pi } { 2 }$ 
B)   $\frac { 3 \pi } { 4 } + \frac { n \pi } { 3 } , \frac { \pi } { 12 } + \frac { n \pi } { 2 }$ 
C)   $\frac { \pi } { 2 } + \frac { n \pi } { 3 } , \frac { \pi } { 12 } + \frac { n \pi } { 2 }$ 
D)   $\frac { 5 \pi } { 12 } + \frac { n \pi } { 3 } , \frac { \pi } { 12 } + \frac { n \pi } { 2 }$ 
E)   $\frac { \pi } { 12 } + \frac { n \pi } { 2 } , \frac { 5 \pi } { 12 } + \frac { n \pi } { 2 }$ 
A)  $\frac { \pi } { 12 } - \frac { n \pi } { 3 } , \frac { 5 \pi } { 12 } + \frac { n \pi } { 2 }$ 
B)   $\frac { 3 \pi } { 4 } + \frac { n \pi } { 3 } , \frac { \pi } { 12 } + \frac { n \pi } { 2 }$ 
C)   $\frac { \pi } { 2 } + \frac { n \pi } { 3 } , \frac { \pi } { 12 } + \frac { n \pi } { 2 }$ 
D)   $\frac { 5 \pi } { 12 } + \frac { n \pi } { 3 } , \frac { \pi } { 12 } + \frac { n \pi } { 2 }$ 
E)   $\frac { \pi } { 12 } + \frac { n \pi } { 2 } , \frac { 5 \pi } { 12 } + \frac { n \pi } { 2 }$

Question 7

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\cos \alpha ( \sec \alpha - \cos \alpha )$

Accepted Answer

A)   $\frac { \csc ^ { 2 } \alpha - \sec ^ { 2 } \alpha + \tan ^ { 2 } \alpha } { \csc ^ { 2 } \alpha }$ 
B)   $1 - \sin ^ { 2 } \alpha$ 
C)   $\frac { \csc ^ { 2 } \alpha - 1 } { \csc ^ { 2 } \alpha }$ 
D)   $1 - \cos ^ { 2 } \alpha$ 
E)   $1 - \cot ^ { 2 } \alpha$ 
A)   $\frac { \csc ^ { 2 } \alpha - \sec ^ { 2 } \alpha + \tan ^ { 2 } \alpha } { \csc ^ { 2 } \alpha }$ 
B)   $1 - \sin ^ { 2 } \alpha$ 
C)   $\frac { \csc ^ { 2 } \alpha - 1 } { \csc ^ { 2 } \alpha }$ 
D)   $1 - \cos ^ { 2 } \alpha$ 
E)   $1 - \cot ^ { 2 } \alpha$

Question 8

Use a calculator to demonstrate the identity for the value of $\theta $. 
 $\sin ( - \theta ) = - \sin \theta , \theta = 258 ^ { \circ }$

Accepted Answer

A)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx 0.9781$ 
B)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx 1.0081$ 
C)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx 0.9981$ 
D)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx - 0.9781$ 
E)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx - 0.9981$ 
A)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx 0.9781$ 
B)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx 1.0081$ 
C)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx 0.9981$ 
D)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx - 0.9781$ 
E)   $\sin \left( - 258 ^ { \circ } \right) = - \sin 258 ^ { \circ } \approx - 0.9981$

Question 9

Use the fundamental identities to simplify the expression. 
 $\frac { \sin \theta } { \tan \theta }$

Accepted Answer

A) cot $\theta $ 
B)   cot $\theta $ . 
C)  sec $\theta $ 
D)  cos $\theta $ .. 
E)  csc $\theta $ 
A) cot $\theta $ 
B)   cot $\theta $ . 
C)  sec $\theta $ 
D)  cos $\theta $ .. 
E)  csc $\theta $

Question 10

Use the trigonometric substitution u = a sin $\theta $, where - $\pi $/2  0 to simplify the expression $\sqrt { a ^ { 2 } - u ^ { 2 } }$ .

Accepted Answer

A)  a csc $\theta $ 
B)  a sin $\theta $ 
C)  a tan $\theta $ 
D)  a cos $\theta $ 
E)  - a cos $\theta $ 
A)  a csc $\theta $ 
B)  a sin $\theta $ 
C)  a tan $\theta $ 
D)  a cos $\theta $ 
E)  - a cos $\theta $

Question 11

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. 
 $( \tan x + 1 ) ^ { 2 }$

Accepted Answer

A)   $\tan ^ { 2 } x + 1$ 
B)   $\sec ^ { 2 } x + 2 \tan x$ 
C)   $\frac { 1 + 2 \sin x \cos x } { \cos ^ { 2 } x }$ 
D)   $\tan ^ { 2 } x + 2 \tan x + 1$ 
E)   $\sec ^ { 2 } x ( 1 + 2 \sin x \cos x )$ 
A)   $\tan ^ { 2 } x + 1$ 
B)   $\sec ^ { 2 } x + 2 \tan x$ 
C)   $\frac { 1 + 2 \sin x \cos x } { \cos ^ { 2 } x }$ 
D)   $\tan ^ { 2 } x + 2 \tan x + 1$ 
E)   $\sec ^ { 2 } x ( 1 + 2 \sin x \cos x )$

Question 12

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ , where $C = \arctan ( a / b ) , a = 13 , b = 6 , B = 3$ to rewrite the trigonometric expression in the following form. 
 $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$   $a \sin B \theta + b \cos B \theta$

Accepted Answer

A) 6 $\cos ( 3 \theta - 1.1384 )$ 
B)  $\sqrt { 205 }$ $\cos ( 3 \theta + 1.1384 )$ 
C)  $\sqrt { 205 }$ $\cos ( 3 \theta - 1.1384 )$ 
D) 13 $\cos ( 3 \theta + 1.1384 )$ 
E) 13 $\cos ( 3 \theta - 1.1384 )$ 
A) 6 $\cos ( 3 \theta - 1.1384 )$ 
B)  $\sqrt { 205 }$ $\cos ( 3 \theta + 1.1384 )$ 
C)  $\sqrt { 205 }$ $\cos ( 3 \theta - 1.1384 )$ 
D) 13 $\cos ( 3 \theta + 1.1384 )$ 
E) 13 $\cos ( 3 \theta - 1.1384 )$

Question 13

Convert the expression.   $3 \csc 2 \theta$

Accepted Answer

A)   $\frac { 3 \csc \theta } { 2 \sin \theta }$ 
B)   $\frac { 3 \csc \theta } { 2 \sec \theta }$ 
C)   $\frac { 3 \csc \theta } { \cos \theta }$ 
D)  $\frac { 3 \csc \theta } { 2 \cos \theta }$ 
E)   $\frac { 3 \sec \theta } { 2 \cos \theta }$ 
A)   $\frac { 3 \csc \theta } { 2 \sin \theta }$ 
B)   $\frac { 3 \csc \theta } { 2 \sec \theta }$ 
C)   $\frac { 3 \csc \theta } { \cos \theta }$ 
D)  $\frac { 3 \csc \theta } { 2 \cos \theta }$ 
E)   $\frac { 3 \sec \theta } { 2 \cos \theta }$

Question 14

Use the cofunction identities to evaluate the expression without using a calculator. ​
Cos235° + cos250° + cos240° + cos255°
​

Accepted Answer

A) -2 
B) 1 
C) -1 
D) 3 
E) 2 
A) -2 
B) 1 
C) -1 
D) 3 
E) 2

Question 15

Use a graphing utility to graph the function.  
  $f ( x ) = \left( \sin ^ { 2 } x - \cos x \right)$

Accepted Answer

A)     
B)    
C)     
D)     
E)    
A)     
B)    
C)     
D)     
E)

Question 16

Which of the following is a solution to the given equation? 
 $2 \cos x - 1 = 0$

Accepted Answer

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

Question 17

Solve the following equation.  $12 \sec ^ { 2 } x - 16 = 0$

Accepted Answer

A)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
B)   $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
C)   $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
D)   $\frac { \pi } { 6 } + n \pi , \frac { 5 \pi } { 6 } + n \pi$ 
E)   $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
A)  $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
B)   $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
C)   $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
D)   $\frac { \pi } { 6 } + n \pi , \frac { 5 \pi } { 6 } + n \pi$ 
E)   $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$

Question 18

Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ .

Accepted Answer

A)   $\sin x + \sec x$ 
B)   $\sin x + 1$ 
C)   $\sin x - \tan x \sec x$ 
D)   $\sin x \sin x$ 
E)   $\csc x \cot x - \sin x$ 
A)   $\sin x + \sec x$ 
B)   $\sin x + 1$ 
C)   $\sin x - \tan x \sec x$ 
D)   $\sin x \sin x$ 
E)   $\csc x \cot x - \sin x$

Question 19

Find the exact value of the given expression.   $\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)$

Accepted Answer

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

Question 20

Solve the multiple-angle equation. $\tan \frac { x } { 2 } = \frac { \sqrt { 3 } } { 3 }$

Accepted Answer

A)   $x = \frac { 5 \pi } { 3 } + n \pi$ 
B)   $x = \frac { 7 \pi } { 6 } + n \pi \text { and } \frac { 11 \pi } { 6 } + n \pi$ 
C)   $x = \frac { 2 \pi } { 3 } + n \pi$ 
D)   $x = \frac { 5 \pi } { 6 } + n \pi \text { and } \frac { 7 \pi } { 6 } + n \pi$ 
E)  $x = \frac { \pi } { 3 } + 2 n \pi$ 
A)   $x = \frac { 5 \pi } { 3 } + n \pi$ 
B)   $x = \frac { 7 \pi } { 6 } + n \pi \text { and } \frac { 11 \pi } { 6 } + n \pi$ 
C)   $x = \frac { 2 \pi } { 3 } + n \pi$ 
D)   $x = \frac { 5 \pi } { 6 } + n \pi \text { and } \frac { 7 \pi } { 6 } + n \pi$ 
E)  $x = \frac { \pi } { 3 } + 2 n \pi$

Which of the following is a solution to the given equation? Cscx - 2 = 0

Solve the following equation. $\sin x ( 5 \sin x + 5 ) = 0$

Find the exact value of the given expression using a sum or difference formula. $\cos \frac { 13 \pi } { 12 }$

Which of the following expressions is equivalent to the given expression $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$ ? ( $\theta$ $\neq$ $\pi$ n, where n is a whole number)

Solve the multiple-angle equation. $2 \sec 4 x = 4$

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\cos \alpha ( \sec \alpha - \cos \alpha )$

Use a calculator to demonstrate the identity for the value of $\theta$ . $\sin ( - \theta ) = - \sin \theta , \theta = 258 ^ { \circ }$

Use the fundamental identities to simplify the expression. $\frac { \sin \theta } { \tan \theta }$

Use the trigonometric substitution u = a sin $\theta$ , where - $\pi$ /2 < $\theta$ < $\pi$ /2 and a > 0 to simplify the expression $\sqrt { a ^ { 2 } - u ^ { 2 } }$ .

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $( \tan x + 1 ) ^ { 2 }$

Convert the expression. $3 \csc 2 \theta$

Use the cofunction identities to evaluate the expression without using a calculator. Cos²35° + cos²50° + cos²40° + cos²55°

Use a graphing utility to graph the function. $f ( x ) = \left( \sin ^ { 2 } x - \cos x \right)$

Which of the following is a solution to the given equation? $2 \cos x - 1 = 0$

Solve the following equation. $12 \sec ^ { 2 } x - 16 = 0$

Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ .

Find the exact value of the given expression. $\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)$

Solve the multiple-angle equation. $\tan \frac { x } { 2 } = \frac { \sqrt { 3 } } { 3 }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 5: Analytic Trigonometry

Which of the following is a solution to the given equation? Cscx - 2 = 0

Solve the following equation. sin⁡x(5sin⁡x+5)=0\sin x ( 5 \sin x + 5 ) = 0sinx(5sinx+5)=0

Find the exact value of the given expression using a sum or difference formula. cos⁡13π12\cos \frac { 13 \pi } { 12 }cos1213π​

Which of the following expressions is equivalent to the given expression 25−25cos⁡θ1+cos⁡θ\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }1+cosθ25−25cosθ​​ ? ( θ\theta θ ≠\neq= π\piπ n, where n is a whole number)

Solve the multiple-angle equation. 2sec⁡4x=42 \sec 4 x = 42sec4x=4

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. cos⁡α(sec⁡α−cos⁡α)\cos \alpha ( \sec \alpha - \cos \alpha )cosα(secα−cosα)

Use a calculator to demonstrate the identity for the value of θ\theta θ . sin⁡(−θ)=−sin⁡θ,θ=258∘\sin ( - \theta ) = - \sin \theta , \theta = 258 ^ { \circ }sin(−θ)=−sinθ,θ=258∘

Use the fundamental identities to simplify the expression. sin⁡θtan⁡θ\frac { \sin \theta } { \tan \theta }tanθsinθ​

Use the trigonometric substitution u = a sin θ\theta θ , where - π\pi π /2 < θ\theta θ < π\pi π /2 and a > 0 to simplify the expression a2−u2\sqrt { a ^ { 2 } - u ^ { 2 } }a2−u2​ .

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. (tan⁡x+1)2( \tan x + 1 ) ^ { 2 }(tanx+1)2

Convert the expression. 3csc⁡2θ3 \csc 2 \theta3csc2θ

Use the cofunction identities to evaluate the expression without using a calculator. ​ Cos235° + cos250° + cos240° + cos255° ​

Use a graphing utility to graph the function. f(x)=(sin⁡2x−cos⁡x)f ( x ) = \left( \sin ^ { 2 } x - \cos x \right)f(x)=(sin2x−cosx)

Which of the following is a solution to the given equation? 2cos⁡x−1=02 \cos x - 1 = 02cosx−1=0

Solve the following equation. 12sec⁡2x−16=012 \sec ^ { 2 } x - 16 = 012sec2x−16=0

Find the rate of change of the function f(x)=−csc⁡x−cos⁡xf ( x ) = - \csc x - \cos xf(x)=−cscx−cosx .

Find the exact value of the given expression. cos⁡(300∘+135∘)\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)cos(300∘+135∘)

Solve the multiple-angle equation. tan⁡x2=33\tan \frac { x } { 2 } = \frac { \sqrt { 3 } } { 3 }tan2x​=33​​

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Solve the following equation. $\sin x ( 5 \sin x + 5 ) = 0$

Find the exact value of the given expression using a sum or difference formula. $\cos \frac { 13 \pi } { 12 }$

Which of the following expressions is equivalent to the given expression $\sqrt { \frac { 25 - 25 \cos \theta } { 1 + \cos \theta } }$ ? ( $\theta$ $\neq$ $\pi$ n, where n is a whole number)

Solve the multiple-angle equation. $2 \sec 4 x = 4$

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\cos \alpha ( \sec \alpha - \cos \alpha )$

Use a calculator to demonstrate the identity for the value of $\theta$ . $\sin ( - \theta ) = - \sin \theta , \theta = 258 ^ { \circ }$

Use the fundamental identities to simplify the expression. $\frac { \sin \theta } { \tan \theta }$

Use the trigonometric substitution u = a sin $\theta$ , where - $\pi$ /2 < $\theta$ < $\pi$ /2 and a > 0 to simplify the expression $\sqrt { a ^ { 2 } - u ^ { 2 } }$ .

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $( \tan x + 1 ) ^ { 2 }$

Convert the expression. $3 \csc 2 \theta$

Use the cofunction identities to evaluate the expression without using a calculator. Cos²35° + cos²50° + cos²40° + cos²55°

Use a graphing utility to graph the function. $f ( x ) = \left( \sin ^ { 2 } x - \cos x \right)$

Which of the following is a solution to the given equation? $2 \cos x - 1 = 0$

Solve the following equation. $12 \sec ^ { 2 } x - 16 = 0$

Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ .

Find the exact value of the given expression. $\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)$

Solve the multiple-angle equation. $\tan \frac { x } { 2 } = \frac { \sqrt { 3 } } { 3 }$