Question 1

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

Accepted Answer

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

Question 2

Which of the following expressions is equivalent to 2 - 4 cos2x + 4 cos4x? ​

Accepted Answer

A) 2 sin2x + 2 cos2x 
B) 2 sin4x - 2 cos2x 
C) 2 sin2x + 2 cos4x 
D) 2 sin4x + 2 cos4x 
E) 2 sin4x - 2 cos4x 
A) 2 sin2x + 2 cos2x 
B) 2 sin4x - 2 cos2x 
C) 2 sin2x + 2 cos4x 
D) 2 sin4x + 2 cos4x 
E) 2 sin4x - 2 cos4x

Question 3

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2$\pi $).   $\cot ^ { 2 } x - 25 = 0$

Accepted Answer

A)  $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + 2 \pi$ 
B)   $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + \pi$ 
C)  $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( - \frac { 1 } { 5 } \right) + \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi$ 
D)   $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + 2 \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi$ 
E)   $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + 2 \pi , \arctan \left( - \frac { 1 } { 5 } \right) + \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi$ 
A)  $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + 2 \pi$ 
B)   $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( \frac { 1 } { 5 } \right) + \pi$ 
C)  $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + \pi , \arctan \left( - \frac { 1 } { 5 } \right) + \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi$ 
D)   $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + 2 \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi$ 
E)   $\arctan \left( \frac { 1 } { 5 } \right) , \arctan \left( \frac { 1 } { 5 } \right) + 2 \pi , \arctan \left( - \frac { 1 } { 5 } \right) + \pi , \arctan \left( - \frac { 1 } { 5 } \right) + 2 \pi$

Question 4

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

Question 5

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 6

Solve the following equation. $\tan ^ { 4 } x - 1 = 0$

Accepted Answer

A)   $x = \frac { \pi } { 2 } + n \pi$ , where n is an integer 
B)  $x = n \pi \text { and } x = \frac { 3 \pi } { 2 } + 2 n \pi$ , where n is an integer 
C)   $x = n \pi \text { and } x = \frac { 3 \pi } { 4 } + n \pi$ , where n is an integer 
D)  $x = \frac { \pi } { 4 } + \frac { n \pi } { 2 }$ , where n is an integer 
E)   $x = n \pi \text { and } x = \frac { \pi } { 2 } + n \pi$ , where n is an integer 
A)   $x = \frac { \pi } { 2 } + n \pi$ , where n is an integer 
B)  $x = n \pi \text { and } x = \frac { 3 \pi } { 2 } + 2 n \pi$ , where n is an integer 
C)   $x = n \pi \text { and } x = \frac { 3 \pi } { 4 } + n \pi$ , where n is an integer 
D)  $x = \frac { \pi } { 4 } + \frac { n \pi } { 2 }$ , where n is an integer 
E)   $x = n \pi \text { and } x = \frac { \pi } { 2 } + n \pi$ , where n is an integer

Question 7

Perform the multiplication and use the fundamental identities to simplify. 
 $( \sin x - \cos x ) ^ { 2 }$

Accepted Answer

A)  $1 + \sin x + \cos x$ 
B)  $2 - 2 \sin x \cos x$ 
C)  $1 - 2 \sin x \cos x$ 
D)  $1 + 2 \sin x + \cos x$ 
E)  $1 - \sin x \cos x$ 
A)  $1 + \sin x + \cos x$ 
B)  $2 - 2 \sin x \cos x$ 
C)  $1 - 2 \sin x \cos x$ 
D)  $1 + 2 \sin x + \cos x$ 
E)  $1 - \sin x \cos x$

Question 8

Use the sum-to-product formulas to rewrite the sum or difference as a product.   $\cos 12 \theta + \cos 8 \theta$

Accepted Answer

A)   $2 \sin 10 \theta \cos 2 \theta$ 
B)   $2 \cos 10 \theta \sin 2 \theta$ 
C)   $2 \sin 12 \theta \cos 8 \theta$ 
D)   $2 \cos 10 \theta \cos 2 \theta$ 
E)   $2 \sin 10 \theta \sin 2 \theta$ 
A)   $2 \sin 10 \theta \cos 2 \theta$ 
B)   $2 \cos 10 \theta \sin 2 \theta$ 
C)   $2 \sin 12 \theta \cos 8 \theta$ 
D)   $2 \cos 10 \theta \cos 2 \theta$ 
E)   $2 \sin 10 \theta \sin 2 \theta$

Question 9

Evaluate the expression. 
 $\frac { 1 } { \tan x + \cot x }$

Accepted Answer

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

Question 10

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​
Sec5x (sec x tan x) - ​sec3x (sec x tan x)
​

Accepted Answer

A) ​sec4x tan x 
B) ​4 sec x tan4 x 
C) ​sec3x tan5x 
D) ​sec4x tan3 x 
E) ​sec3x tan3x 
A) ​sec4x tan x 
B) ​4 sec x tan4 x 
C) ​sec3x tan5x 
D) ​sec4x tan3 x 
E) ​sec3x tan3x

Question 11

Evaluate the following expression.(t $\neq$  $\pi$/2+$\pi$n, where n is a whole number) 
 $2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)$

Accepted Answer

A) - 2 tan t 
B) 2 tan t 
C) 2 sin t 
D) - 2 cot t 
E) 2 cot t 
A) - 2 tan t 
B) 2 tan t 
C) 2 sin t 
D) - 2 cot t 
E) 2 cot t

Question 12

Evaluate the following expression. 
 $$\frac { \cos 2 x - \cos 2 y } { \sin 2 x + \sin 2 y } + \frac { \sin 2 x - \sin 2 y } { \cos 2 x + \cos 2 y }$$

Accepted Answer

A) 1 
B) 2 
C) -2 
D) 0 
E) - 1 
A) 1 
B) 2 
C) -2 
D) 0 
E) - 1

Question 13

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x.
 $$\sin x = \frac { 1 } { 5 }$$ , $$\cos x > 0$$

Accepted Answer

A)   $\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
B)   $\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = - \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
C)   $\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = - 5 \
\tan x = - \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
D)   $\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
E)   $\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = \frac { 1 } { 5 } \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
A)   $\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
B)   $\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = - \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
C)   $\begin{array} { l } 
\cos x = - \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = - 5 \
\tan x = - \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
D)   $\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = 5 \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$ 
E)   $\begin{array} { l } 
\cos x = \frac { 2 \sqrt { 6 } } { 5 } \
\csc x = \frac { 1 } { 5 } \
\tan x = \frac { \sqrt { 6 } } { 12 }
\end{array}$

Question 14

Evaluate the following expression.(x $\neq$ $\pi$/10 + $\pi$n, where n is a whole number) 
 $5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }$

Accepted Answer

A)  $\frac { 10 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
B)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$ 
C)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
D)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
E)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$ 
A)  $\frac { 10 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
B)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$ 
C)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
D)  $\frac { - 5 \sin 5 x \cos 5 x } { \sin 5 x - \cos 5 x }$ 
E)  $\frac { 5 \sin 5 x \cos 5 x } { \sin 5 x + \cos 5 x }$

Question 15

Simplify the following expression algebraically. 
 $4 \sin \left( \frac { 3 \pi } { 2 } + \theta \right)$

Accepted Answer

A)  $\frac { 3 } { 2 } \cos \theta$ 
B)  $4 \cos \theta$ 
C)  $- 4 \sin \theta$ 
D)  $- \frac { 3 } { 2 } \cos \theta$ 
E)  $- 4 \cos \theta$ 
A)  $\frac { 3 } { 2 } \cos \theta$ 
B)  $4 \cos \theta$ 
C)  $- 4 \sin \theta$ 
D)  $- \frac { 3 } { 2 } \cos \theta$ 
E)  $- 4 \cos \theta$

Question 16

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2$\pi $).
 $\sin 2 x + 1.5 \cos x = 0$

Accepted Answer

A) x = 1.624, 1.932, 5.776, 5.997 
B)  x = 1.101, 2.118, 3.982, 5.104 
C)  x = 1.571, 3.990, 4.712, 5.435 
D)  x = 1.055, 3.785, 4.652, 5.721 
E)  x = 1.484, 3.799, 4.626, 5.490 
A) x = 1.624, 1.932, 5.776, 5.997 
B)  x = 1.101, 2.118, 3.982, 5.104 
C)  x = 1.571, 3.990, 4.712, 5.435 
D)  x = 1.055, 3.785, 4.652, 5.721 
E)  x = 1.484, 3.799, 4.626, 5.490

Question 17

Find the expression as the sine of an angle. 
 $\sin 5 \cos 1.7 - \cos 5 \sin 1.7$

Accepted Answer

A)  $\sin 3.4$ 
B)  $\sin 3.3$ 
C)  $\sin 3.5$ 
D)  $\sin 3.7$ 
E)  $\sin 3.6$ 
A)  $\sin 3.4$ 
B)  $\sin 3.3$ 
C)  $\sin 3.5$ 
D)  $\sin 3.7$ 
E)  $\sin 3.6$

Question 18

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 19

Convert the expression.  
  $( 2 \sin x + 2 \cos x ) ^ { 2 }$

Accepted Answer

A)   $4 - 4 \sin 2 x$ 
B)   $2 + 4 \sin x$ 
C)   $4 + 4 \sin x$ 
D)   $4 - 4 \sin x$ 
E)   $4 + 4 \sin 2 x$ 
A)   $4 - 4 \sin 2 x$ 
B)   $2 + 4 \sin x$ 
C)   $4 + 4 \sin x$ 
D)   $4 - 4 \sin x$ 
E)   $4 + 4 \sin 2 x$

Question 20

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. 
 $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$

Accepted Answer

A)   $\cos ^ { 2 } x - \cos ^ { 2 } x \sin x$ 
B)   $\frac { 1 - \sin x } { \sec ^ { 2 } x }$ 
C)   $\frac { \cos ^ { 4 } x } { 1 + \sin x }$ 
D)   $\cos ^ { 2 } x ( 1 - \sin x )$ 
E)  $\frac { 1 + \cos ^ { 2 } x } { \sin x }$ 
A)   $\cos ^ { 2 } x - \cos ^ { 2 } x \sin x$ 
B)   $\frac { 1 - \sin x } { \sec ^ { 2 } x }$ 
C)   $\frac { \cos ^ { 4 } x } { 1 + \sin x }$ 
D)   $\cos ^ { 2 } x ( 1 - \sin x )$ 
E)  $\frac { 1 + \cos ^ { 2 } x } { \sin x }$

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

Which of the following expressions is equivalent to 2 - 4 cos²x + 4 cos⁴x?

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 $\pi$ ). $\cot ^ { 2 } x - 25 = 0$

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. $\tan ^ { 4 } x - 1 = 0$

Perform the multiplication and use the fundamental identities to simplify. $( \sin x - \cos x ) ^ { 2 }$

Use the sum-to-product formulas to rewrite the sum or difference as a product. $\cos 12 \theta + \cos 8 \theta$

Evaluate the expression. $\frac { 1 } { \tan x + \cot x }$

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) Sec⁵x (sec x tan x) - sec³x (sec x tan x)

Evaluate the following expression.(t $\neq$ $\pi$ /2+ $\pi$ n, where n is a whole number) $2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)$

Evaluate the following expression. $\frac { \cos 2 x - \cos 2 y } { \sin 2 x + \sin 2 y } + \frac { \sin 2 x - \sin 2 y } { \cos 2 x + \cos 2 y }$

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x. $\sin x = \frac { 1 } { 5 }$ , $\cos x > 0$

Evaluate the following expression.(x $\neq$ $\pi$ /10 + $\pi$ n, where n is a whole number) $5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }$

Simplify the following expression algebraically. $4 \sin \left( \frac { 3 \pi } { 2 } + \theta \right)$

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2 $\pi$ ). $\sin 2 x + 1.5 \cos x = 0$

Find the expression as the sine of an angle. $\sin 5 \cos 1.7 - \cos 5 \sin 1.7$

Convert the expression. $( 2 \sin x + 2 \cos x ) ^ { 2 }$

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Additional Topics In Trigonometery

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Limits and An Introduction To Calculus

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Exam 5: Analytic Trigonometry

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

Which of the following expressions is equivalent to 2 - 4 cos2x + 4 cos4x? ​

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 π\pi π ). cot⁡2x−25=0\cot ^ { 2 } x - 25 = 0cot2x−25=0

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. tan⁡4x−1=0\tan ^ { 4 } x - 1 = 0tan4x−1=0

Perform the multiplication and use the fundamental identities to simplify. (sin⁡x−cos⁡x)2( \sin x - \cos x ) ^ { 2 }(sinx−cosx)2

Use the sum-to-product formulas to rewrite the sum or difference as a product. cos⁡12θ+cos⁡8θ\cos 12 \theta + \cos 8 \thetacos12θ+cos8θ

Evaluate the expression. 1tan⁡x+cot⁡x\frac { 1 } { \tan x + \cot x }tanx+cotx1​

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​ Sec5x (sec x tan x) - ​sec3x (sec x tan x) ​

Evaluate the following expression.(t ≠\neq= π\piπ /2+ π\piπ n, where n is a whole number) 2sin⁡tcsc⁡(π2−t)2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)2sintcsc(2π​−t)

Evaluate the following expression. cos⁡2x−cos⁡2ysin⁡2x+sin⁡2y+sin⁡2x−sin⁡2ycos⁡2x+cos⁡2y\frac { \cos 2 x - \cos 2 y } { \sin 2 x + \sin 2 y } + \frac { \sin 2 x - \sin 2 y } { \cos 2 x + \cos 2 y }sin2x+sin2ycos2x−cos2y​+cos2x+cos2ysin2x−sin2y​

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x. sin⁡x=15\sin x = \frac { 1 } { 5 }sinx=51​ , cos⁡x>0\cos x > 0cosx>0

Evaluate the following expression.(x ≠\neq= π\piπ /10 + π\piπ n, where n is a whole number) 5cos⁡5x−5cos⁡5x1−tan⁡5x5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }5cos5x−1−tan5x5cos5x​

Simplify the following expression algebraically. 4sin⁡(3π2+θ)4 \sin \left( \frac { 3 \pi } { 2 } + \theta \right)4sin(23π​+θ)

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2 π\pi π ). sin⁡2x+1.5cos⁡x=0\sin 2 x + 1.5 \cos x = 0sin2x+1.5cosx=0

Find the expression as the sine of an angle. sin⁡5cos⁡1.7−cos⁡5sin⁡1.7\sin 5 \cos 1.7 - \cos 5 \sin 1.7sin5cos1.7−cos5sin1.7

Convert the expression. (2sin⁡x+2cos⁡x)2( 2 \sin x + 2 \cos x ) ^ { 2 }(2sinx+2cosx)2

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. sin⁡3x−sin⁡2x−sin⁡x+1\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1sin3x−sin2x−sinx+1

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

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

Which of the following expressions is equivalent to 2 - 4 cos²x + 4 cos⁴x?

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 $\pi$ ). $\cot ^ { 2 } x - 25 = 0$

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. $\tan ^ { 4 } x - 1 = 0$

Perform the multiplication and use the fundamental identities to simplify. $( \sin x - \cos x ) ^ { 2 }$

Use the sum-to-product formulas to rewrite the sum or difference as a product. $\cos 12 \theta + \cos 8 \theta$

Evaluate the expression. $\frac { 1 } { \tan x + \cot x }$

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) Sec⁵x (sec x tan x) - sec³x (sec x tan x)

Evaluate the following expression.(t $\neq$ $\pi$ /2+ $\pi$ n, where n is a whole number) $2 \sin t \csc \left( \frac { \pi } { 2 } - t \right)$

Evaluate the following expression. $\frac { \cos 2 x - \cos 2 y } { \sin 2 x + \sin 2 y } + \frac { \sin 2 x - \sin 2 y } { \cos 2 x + \cos 2 y }$

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x. $\sin x = \frac { 1 } { 5 }$ , $\cos x > 0$

Evaluate the following expression.(x $\neq$ $\pi$ /10 + $\pi$ n, where n is a whole number) $5 \cos 5 x - \frac { 5 \cos 5 x } { 1 - \tan 5 x }$

Simplify the following expression algebraically. $4 \sin \left( \frac { 3 \pi } { 2 } + \theta \right)$

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2 $\pi$ ). $\sin 2 x + 1.5 \cos x = 0$

Find the expression as the sine of an angle. $\sin 5 \cos 1.7 - \cos 5 \sin 1.7$

Convert the expression. $( 2 \sin x + 2 \cos x ) ^ { 2 }$

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. $\sin ^ { 3 } x - \sin ^ { 2 } x - \sin x + 1$