Question 1

Use the half-angle formulas to simplify the expression.   $- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$

Accepted Answer

A)   $- \left| \sin \left( \frac { x - 3 } { 2 } \right) \right|$ 
B)   $- \left| \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right) \right|$ 
C)   $- | \sin ( x - 3 ) |$ 
D)   $- \left| \sin ^ { - 1 } \left( \frac { x - 3 } { 2 } \right) \right|$ 
E)   $- \left| \sin \left( \frac { x + 3 } { 2 } \right) \right|$ 
A)   $- \left| \sin \left( \frac { x - 3 } { 2 } \right) \right|$ 
B)   $- \left| \sin ^ { - 1 } \left( \frac { x + 3 } { 2 } \right) \right|$ 
C)   $- | \sin ( x - 3 ) |$ 
D)   $- \left| \sin ^ { - 1 } \left( \frac { x - 3 } { 2 } \right) \right|$ 
E)   $- \left| \sin \left( \frac { x + 3 } { 2 } \right) \right|$

Question 2

Solve the multiple-angle equation. 
 $4 \tan 3 x = 4$

Accepted Answer

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

Question 3

Find all solutions of the following equation in the interval [0, 2$\pi $). 
 $3 \sec x - 3 \tan x = 3$

Accepted Answer

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

Question 4

Use the sum-to-product formulas to find the exact value of the given expression.  
  $\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$

Accepted Answer

A)   $\frac { - \sqrt { 3 } } { 2 }$ 
B)  1 
C)   $\frac { \sqrt { 3 } } { 2 }$ 
D) -1 
E) 0 
A)   $\frac { - \sqrt { 3 } } { 2 }$ 
B)  1 
C)   $\frac { \sqrt { 3 } } { 2 }$ 
D) -1 
E) 0

Question 5

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. $\frac { \csc x - \sin x } { \cot x }$

Accepted Answer

A)  y = cos x2- 2    2   $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 2 
B)  y = sin x2- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 2 
C)  y = csc x4- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 4 
D)  y = cot x4- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 4 
E)  y = tan x4- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 4 
A)  y = cos x2- 2    2   $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 2 
B)  y = sin x2- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 2 
C)  y = csc x4- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 4 
D)  y = cot x4- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 4 
E)  y = tan x4- 2    2  $X _ { \text {scl } } = \frac { \pi } { 2 }$ - 4

Question 6

Use the Quadratic Formula to solve the given equation on the interval [ $0 , \frac { \pi } { 2 }$ ); then use a graphing utility to approximate the angle x.Round answers to three decimal places.  $75 \cos ^ { 2 } x - 34 \cos x + 3 = 0$

Accepted Answer

A) x = 1.229, 1.433 
B)  x = 1.227, 1.422 
C)  x = 1.233, 1.469 
D)  x = 1.231, 1.451 
E)  x = 1.235, 1.480 
A) x = 1.229, 1.433 
B)  x = 1.227, 1.422 
C)  x = 1.233, 1.469 
D)  x = 1.231, 1.451 
E)  x = 1.235, 1.480

Question 7

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​
(tan5x + tan7x) sec2x
​

Accepted Answer

A) sec4x tan12x 
B) sec4x tan5x 
C) 7 sec4x tan5x 
D) 5 sec4x tan5x 
E) sec12x tan5x 
A) sec4x tan12x 
B) sec4x tan5x 
C) 7 sec4x tan5x 
D) 5 sec4x tan5x 
E) sec12x tan5x

Question 8

Evaluate the following expression. ​
2(1 + sin α)(1 - sin α)
​

Accepted Answer

A) -3 sin2 α 
B) 3 cos2 α 
C) -2 cos2 α 
D) 2 sin2 α 
E) 2 cos2 α 
A) -3 sin2 α 
B) 3 cos2 α 
C) -2 cos2 α 
D) 2 sin2 α 
E) 2 cos2 α

Question 9

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

Accepted Answer

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

Question 10

Use a graphing utility to graph the function. 
 $f ( x ) = 5 \left( \sin ^ { 2 } x + \cos x \right)$

Accepted Answer

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

Question 11

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. 
 $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$

Accepted Answer

A)  -1 
B)   $\frac { \cos x } { \sin x }$ 
C)  cot x 
D)  1/ tan x 
E)  cos x csc x 
A)  -1 
B)   $\frac { \cos x } { \sin x }$ 
C)  cot x 
D)  1/ tan x 
E)  cos x csc x

Question 12

Solve the following equation. 
 $4 \cos x + 2 = 0$

Accepted Answer

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

Question 13

Use a graphing utility to graph the function. 
 $f ( x ) = 1.1 ( 2 \sin x + \cos 2 x )$

Accepted Answer

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

Question 14

Simplify the following expression algebraically. 
 $\cos \left( \frac { 3 \pi } { 2 } - x \right)$

Accepted Answer

A)  $\sin x$ 
B)  $\frac { 3 } { 2 } \sin x$ 
C)  $- \cos x$ 
D)  $- \sin x$ 
E)  $- \frac { 3 } { 2 } \sin x$ 
A)  $\sin x$ 
B)  $\frac { 3 } { 2 } \sin x$ 
C)  $- \cos x$ 
D)  $- \sin x$ 
E)  $- \frac { 3 } { 2 } \sin x$

Question 15

Solve the following equation.  
  $10 \sin x + 5 = 0$

Accepted Answer

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

Question 16

Simplify the expression algebraically. $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$

Accepted Answer

A)  $\frac { 4 - 4 \tan \theta } { 1 + \tan \theta }$ 
B)  $\frac { 4 - 4 \tan \theta } { \tan \theta }$ 
C)  $\frac { \tan \theta } { 4 - \tan \theta }$ 
D)  $\frac { 4 + 4 \tan \theta } { 1 - \tan \theta }$ 
E)  $\frac { 4 + 4 \tan \theta } { \tan \theta }$ 
A)  $\frac { 4 - 4 \tan \theta } { 1 + \tan \theta }$ 
B)  $\frac { 4 - 4 \tan \theta } { \tan \theta }$ 
C)  $\frac { \tan \theta } { 4 - \tan \theta }$ 
D)  $\frac { 4 + 4 \tan \theta } { 1 - \tan \theta }$ 
E)  $\frac { 4 + 4 \tan \theta } { \tan \theta }$

Question 17

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 3 } { 5 }$ and $\cos v = - \frac { 24 } { 25 }$ .(Both u and v are in Quadrant II.)

Accepted Answer

A)  $\sin ( u + v ) = - \frac { 44 } { 125 }$ 
B)  $\sin ( u + v ) = - \frac { 3 } { 5 }$ 
C)  $\sin ( u + v ) = \frac { 4 } { 5 }$ 
D)  $\sin ( u + v ) = - \frac { 4 } { 5 }$ 
E)  $\sin ( u + v ) = \frac { 44 } { 125 }$ 
A)  $\sin ( u + v ) = - \frac { 44 } { 125 }$ 
B)  $\sin ( u + v ) = - \frac { 3 } { 5 }$ 
C)  $\sin ( u + v ) = \frac { 4 } { 5 }$ 
D)  $\sin ( u + v ) = - \frac { 4 } { 5 }$ 
E)  $\sin ( u + v ) = \frac { 44 } { 125 }$

Question 18

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta $, where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .Then find sin $\theta $ and cos $\theta $. 
 $4 = \sqrt { 64 - x ^ { 2 } } , x = 8 \sin \theta$

Accepted Answer

A)   $64 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
B)   $64 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
C)   $8 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
D)   $8 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
E)   $8 \cos \theta = 4 ; \sin \theta = \frac { 1 } { 2 } ; \cos \theta = \pm \frac { \sqrt { 3 } } { 2 }$ 
A)   $64 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
B)   $64 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
C)   $8 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
D)   $8 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }$ 
E)   $8 \cos \theta = 4 ; \sin \theta = \frac { 1 } { 2 } ; \cos \theta = \pm \frac { \sqrt { 3 } } { 2 }$

Question 19

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ .  
  $6 \sin 2 x - 8 \cos x + 9 \sin x = 6$

Accepted Answer

A)  x = 0.398 
B)   x = 1.336 
C)  x = 0.094 
D)   x = 0.73 
E)  x = 0.139 
A)  x = 0.398 
B)   x = 1.336 
C)  x = 0.094 
D)   x = 0.73 
E)  x = 0.139

Question 20

Use the product-to-sum formulas to rewrite the product as a sum or difference.   $10 \cos 45 ^ { \circ } \cos 20 ^ { \circ }$

Accepted Answer

A)   $10 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$ 
B)   $\cos 25 ^ { \circ } + \cos 65 ^ { \circ }$ 
C)   $5 \left( \cos 65 ^ { \circ } - \cos 25 ^ { \circ } \right)$ 
D)  $5 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$ 
E)   $5 \left( \cos 65 ^ { \circ } + \sin 25 ^ { \circ } \right)$ 
A)   $10 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$ 
B)   $\cos 25 ^ { \circ } + \cos 65 ^ { \circ }$ 
C)   $5 \left( \cos 65 ^ { \circ } - \cos 25 ^ { \circ } \right)$ 
D)  $5 \left( \cos 25 ^ { \circ } + \cos 65 ^ { \circ } \right)$ 
E)   $5 \left( \cos 65 ^ { \circ } + \sin 25 ^ { \circ } \right)$

Use the half-angle formulas to simplify the expression. $- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$

Solve the multiple-angle equation. $4 \tan 3 x = 4$

Find all solutions of the following equation in the interval [0, 2 $\pi$ ). $3 \sec x - 3 \tan x = 3$

Use the sum-to-product formulas to find the exact value of the given expression. $\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. $\frac { \csc x - \sin x } { \cot x }$

Use the Quadratic Formula to solve the given equation on the interval [ $0 , \frac { \pi } { 2 }$ ); then use a graphing utility to approximate the angle x.Round answers to three decimal places. $75 \cos ^ { 2 } x - 34 \cos x + 3 = 0$

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) (tan⁵x + tan⁷x) sec²x

Evaluate the following expression. 2(1 + sin α)(1 - sin α)

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

Use a graphing utility to graph the function. $f ( x ) = 5 \left( \sin ^ { 2 } x + \cos x \right)$

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$

Solve the following equation. $4 \cos x + 2 = 0$

Use a graphing utility to graph the function. $f ( x ) = 1.1 ( 2 \sin x + \cos 2 x )$

Simplify the following expression algebraically. $\cos \left( \frac { 3 \pi } { 2 } - x \right)$

Solve the following equation. $10 \sin x + 5 = 0$

Simplify the expression algebraically. $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 3 } { 5 }$ and $\cos v = - \frac { 24 } { 25 }$ .(Both u and v are in Quadrant II.)

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .Then find sin $\theta$ and cos $\theta$ . $4 = \sqrt { 64 - x ^ { 2 } } , x = 8 \sin \theta$

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ . $6 \sin 2 x - 8 \cos x + 9 \sin x = 6$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $10 \cos 45 ^ { \circ } \cos 20 ^ { \circ }$

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

Use the half-angle formulas to simplify the expression. −1−cos⁡(x−3)2- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }−21−cos(x−3)​​

Solve the multiple-angle equation. 4tan⁡3x=44 \tan 3 x = 44tan3x=4

Find all solutions of the following equation in the interval [0, 2 π\pi π ). 3sec⁡x−3tan⁡x=33 \sec x - 3 \tan x = 33secx−3tanx=3

Use the sum-to-product formulas to find the exact value of the given expression. cos⁡150∘+cos⁡30∘\cos 150 ^ { \circ } + \cos 30 ^ { \circ }cos150∘+cos30∘

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. csc⁡x−sin⁡xcot⁡x\frac { \csc x - \sin x } { \cot x }cotxcscx−sinx​

Use the Quadratic Formula to solve the given equation on the interval [ 0,π20 , \frac { \pi } { 2 }0,2π​ ); then use a graphing utility to approximate the angle x.Round answers to three decimal places. 75cos⁡2x−34cos⁡x+3=075 \cos ^ { 2 } x - 34 \cos x + 3 = 075cos2x−34cosx+3=0

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​ (tan5x + tan7x) sec2x ​

Evaluate the following expression. ​ 2(1 + sin α)(1 - sin α) ​

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. sin⁡α(csc⁡α−sin⁡α)\sin \alpha ( \csc \alpha - \sin \alpha )sinα(cscα−sinα)

Use a graphing utility to graph the function. f(x)=5(sin⁡2x+cos⁡x)f ( x ) = 5 \left( \sin ^ { 2 } x + \cos x \right)f(x)=5(sin2x+cosx)

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. sin⁡(π2−x)csc⁡x\sin \left( \frac { \pi } { 2 } - x \right) \csc xsin(2π​−x)cscx

Solve the following equation. 4cos⁡x+2=04 \cos x + 2 = 04cosx+2=0

Use a graphing utility to graph the function. f(x)=1.1(2sin⁡x+cos⁡2x)f ( x ) = 1.1 ( 2 \sin x + \cos 2 x )f(x)=1.1(2sinx+cos2x)

Simplify the following expression algebraically. cos⁡(3π2−x)\cos \left( \frac { 3 \pi } { 2 } - x \right)cos(23π​−x)

Solve the following equation. 10sin⁡x+5=010 \sin x + 5 = 010sinx+5=0

Simplify the expression algebraically. 4tan⁡(π4−θ)4 \tan \left( \frac { \pi } { 4 } - \theta \right)4tan(4π​−θ)

Find the exact value of sin⁡(u+v)\sin ( u + v )sin(u+v) given that sin⁡u=35\sin u = \frac { 3 } { 5 }sinu=53​ and cos⁡v=−2425\cos v = - \frac { 24 } { 25 }cosv=−2524​ .(Both u and v are in Quadrant II.)

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval (−π2,π2)\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)(−2π​,2π​) . 6sin⁡2x−8cos⁡x+9sin⁡x=66 \sin 2 x - 8 \cos x + 9 \sin x = 66sin2x−8cosx+9sinx=6

Use the product-to-sum formulas to rewrite the product as a sum or difference. 10cos⁡45∘cos⁡20∘10 \cos 45 ^ { \circ } \cos 20 ^ { \circ }10cos45∘cos20∘

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

Use the half-angle formulas to simplify the expression. $- \sqrt { \frac { 1 - \cos ( x - 3 ) } { 2 } }$

Solve the multiple-angle equation. $4 \tan 3 x = 4$

Find all solutions of the following equation in the interval [0, 2 $\pi$ ). $3 \sec x - 3 \tan x = 3$

Use the sum-to-product formulas to find the exact value of the given expression. $\cos 150 ^ { \circ } + \cos 30 ^ { \circ }$

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression. $\frac { \csc x - \sin x } { \cot x }$

Use the Quadratic Formula to solve the given equation on the interval [ $0 , \frac { \pi } { 2 }$ ); then use a graphing utility to approximate the angle x.Round answers to three decimal places. $75 \cos ^ { 2 } x - 34 \cos x + 3 = 0$

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) (tan⁵x + tan⁷x) sec²x

Evaluate the following expression. 2(1 + sin α)(1 - sin α)

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

Use a graphing utility to graph the function. $f ( x ) = 5 \left( \sin ^ { 2 } x + \cos x \right)$

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. $\sin \left( \frac { \pi } { 2 } - x \right) \csc x$

Solve the following equation. $4 \cos x + 2 = 0$

Use a graphing utility to graph the function. $f ( x ) = 1.1 ( 2 \sin x + \cos 2 x )$

Simplify the following expression algebraically. $\cos \left( \frac { 3 \pi } { 2 } - x \right)$

Solve the following equation. $10 \sin x + 5 = 0$

Simplify the expression algebraically. $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 3 } { 5 }$ and $\cos v = - \frac { 24 } { 25 }$ .(Both u and v are in Quadrant II.)

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ . $6 \sin 2 x - 8 \cos x + 9 \sin x = 6$

Use the product-to-sum formulas to rewrite the product as a sum or difference. $10 \cos 45 ^ { \circ } \cos 20 ^ { \circ }$