Question 1

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).​ $\csc ^ { 2 } x - 7 \csc x = 0$ ​

Accepted Answer

A) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + \pi , \arcsin \left( - \frac { 1 } { 7 } \right)$ 
B) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + \pi , \arcsin \left( \frac { 1 } { 7 } \right)$ 
C) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + \pi , \arcsin \left( \frac { 1 } { 7 } \right) + 2 \pi$ 
D) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + 2 \pi , \arcsin \left( \frac { 1 } { 7 } \right)$ 
E) ​ $\arcsin \left( \frac { 1 } { 7 } \right) + \pi , \arcsin \left( \frac { 1 } { 7 } \right)$ 
A) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + \pi , \arcsin \left( - \frac { 1 } { 7 } \right)$ 
B) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + \pi , \arcsin \left( \frac { 1 } { 7 } \right)$ 
C) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + \pi , \arcsin \left( \frac { 1 } { 7 } \right) + 2 \pi$ 
D) ​ $\arcsin \left( - \frac { 1 } { 7 } \right) + 2 \pi , \arcsin \left( \frac { 1 } { 7 } \right)$ 
E) ​ $\arcsin \left( \frac { 1 } { 7 } \right) + \pi , \arcsin \left( \frac { 1 } { 7 } \right)$

Question 2

Using the grid provided,sketch the graph of the given function in the interval (-5,5)and then determine the x-intercepts,if any. $$y = \sin \left( \frac { \pi x } { 2 } \right) - 1$$

Accepted Answer

A) (-3,0)and (1,0) 
B) (-2,0) 
C) (-2,0)and (2,0) 
D) no x-intercepts 
E) (-4,0), (0,0),and (4,0) 
A) (-3,0)and (1,0) 
B) (-2,0) 
C) (-2,0)and (2,0) 
D) no x-intercepts 
E) (-4,0), (0,0),and (4,0)

Question 3

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

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 4

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 5

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by $y = \frac { 1 } { 12 } ( \cos 7 t - 3 \sin 7 t )$ ,where y is the displacement (in meters)and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0)for $0 \leq t \leq 1$ .​   ​ ​

Accepted Answer

A) 0.05sec,0.49sec,0.94sec 
B) 0.05sec,0.05sec,0.94sec 
C) -0.40sec,0.49sec,0.94sec 
D) -0.40sec,0.49sec,-0.40sec 
E) 0.05sec,-0.40sec,0.94sec 
A) 0.05sec,0.49sec,0.94sec 
B) 0.05sec,0.05sec,0.94sec 
C) -0.40sec,0.49sec,0.94sec 
D) -0.40sec,0.49sec,-0.40sec 
E) 0.05sec,-0.40sec,0.94sec

Question 6

Solve the following equation.​ $2 \sin ^ { 2 } x = 6 \cos ^ { 2 } x$ ​

Accepted Answer

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

Question 7

Solve the following equation.​ $\cos ^ { 2 } x + \cos x = 0$ ​

Accepted Answer

A) ​ $x = \frac { 3 \pi } { 4 } + n \pi \text { and } x = \frac { 5 \pi } { 4 } + n \pi$ ,where n is an integer 
B) ​ $x = \pi + 2 n \pi \text { and } x = \frac { \pi } { 2 } + n \pi$ ,where n is an integer 
C) ​ $x = \frac { 3 \pi } { 4 } + 2 n \pi \text { and } x = \frac { 5 \pi } { 4 } + 2 n \pi$ ,where n is an integer 
D) ​ $x = n \pi \text { and } x = \frac { 3 \pi } { 2 } + n \pi$ ,where n is an integer 
E) ​ $x = \pi + n \pi \text { and } x = \frac { \pi } { 2 } + 2 n \pi$ ,where n is an integer 
A) ​ $x = \frac { 3 \pi } { 4 } + n \pi \text { and } x = \frac { 5 \pi } { 4 } + n \pi$ ,where n is an integer 
B) ​ $x = \pi + 2 n \pi \text { and } x = \frac { \pi } { 2 } + n \pi$ ,where n is an integer 
C) ​ $x = \frac { 3 \pi } { 4 } + 2 n \pi \text { and } x = \frac { 5 \pi } { 4 } + 2 n \pi$ ,where n is an integer 
D) ​ $x = n \pi \text { and } x = \frac { 3 \pi } { 2 } + n \pi$ ,where n is an integer 
E) ​ $x = \pi + n \pi \text { and } x = \frac { \pi } { 2 } + 2 n \pi$ ,where n is an integer

Question 8

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 9

Find all solutions of the following equation in the interval [0,2π).​ $15 \tan ^ { 3 } x = 5 \tan x$ ​

Accepted Answer

A) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { n \pi } { 6 } , \frac { 2 n \pi } { 6 } , \frac { 3 n \pi } { 6 }$ 
B) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 3 \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 }$ 
C) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 2 \pi } { 6 } , \frac { 3 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
E) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { \pi } { 6 } , \frac { 13 \pi } { 6 }$ 
A) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { n \pi } { 6 } , \frac { 2 n \pi } { 6 } , \frac { 3 n \pi } { 6 }$ 
B) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 3 \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 }$ 
C) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
D) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 2 \pi } { 6 } , \frac { 3 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
E) ​ $0 , \pi , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { \pi } { 6 } , \frac { 13 \pi } { 6 }$

Question 10

The horizontal distance d (in feet)traveled by a projectile with an initial speed of v feet per second is modeled by $d = \frac { v ^ { 2 } } { 32 } \sin 2 \theta$ , where θ is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of $\theta = 60 ^ { \circ }$ .Round to the nearest foot.

Accepted Answer

A) 260 
B) 346 
C) 173 
D) 303 
E) 87 
A) 260 
B) 346 
C) 173 
D) 303 
E) 87

Question 11

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 12

Find all solutions of the following equation in the interval [0,2π).​ $\sin ^ { 3 } x = \sin x$ ​

Accepted Answer

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

Question 13

Find all solutions of the following equation in the interval [0,2π).​ $\sin x - 3 = \cos x - 3$ ​

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Find all solutions of the following equation in the interval [0,2π).​ $5 \sec ^ { 2 } x - 5 = 0$ ​

Accepted Answer

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

Question 16

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 17

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 18

Use a graphing utility to graph the function.​ $$f ( x ) = \sin x - \cos x$$ ​

Accepted Answer

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

Question 19

Solve the following equation.​ $2 \tan ^ { 2 } 3 x = 6$ ​

Accepted Answer

A)  $\frac { 4 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
B) ​ $\frac { \pi } { 2 } + n \pi , \frac { 2 \pi } { 5 } + n \pi$ 
C) ​ $\frac { 2 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
D) ​ $\frac { \pi } { 9 } + \frac { n \pi } { 3 } , \frac { 2 \pi } { 9 } + \frac { n \pi } { 3 }$ 
E) ​ $\frac { \pi } { 3 } + n \pi , \frac { \pi } { 3 } + n \pi$ 
A)  $\frac { 4 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
B) ​ $\frac { \pi } { 2 } + n \pi , \frac { 2 \pi } { 5 } + n \pi$ 
C) ​ $\frac { 2 \pi } { 3 } + n \pi , \frac { 2 \pi } { 3 } + n \pi$ 
D) ​ $\frac { \pi } { 9 } + \frac { n \pi } { 3 } , \frac { 2 \pi } { 9 } + \frac { n \pi } { 3 }$ 
E) ​ $\frac { \pi } { 3 } + n \pi , \frac { \pi } { 3 } + n \pi$

Question 20

Find all solutions of the following equation in the interval [0,2π).​ $3 \sin x + \csc x = 0$ ​

Accepted Answer

A)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
B) No solution 
C) ​ $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
D) ​ $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
E) ​ $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
A)  $\frac { 5 \pi } { 2 } + 2 \pi , \frac { 5 \pi } { 2 } + 2 \pi$ 
B) No solution 
C) ​ $\frac { \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
D) ​ $\frac { 3 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$ 
E) ​ $\frac { 7 \pi } { 2 } + 2 \pi , \frac { 3 \pi } { 2 } + 2 \pi$

Exam 33: Solving Trigonometric Equations

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).​ csc⁡2x−7csc⁡x=0\csc ^ { 2 } x - 7 \csc x = 0csc2x−7cscx=0 ​

Using the grid provided,sketch the graph of the given function in the interval (-5,5)and then determine the x-intercepts,if any. y=sin⁡(πx2)−1y = \sin \left( \frac { \pi x } { 2 } \right) - 1y=sin(2πx​)−1

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

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

Solve the following equation.​ 2sin⁡2x=6cos⁡2x2 \sin ^ { 2 } x = 6 \cos ^ { 2 } x2sin2x=6cos2x ​

Solve the following equation.​ cos⁡2x+cos⁡x=0\cos ^ { 2 } x + \cos x = 0cos2x+cosx=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) ​

Find all solutions of the following equation in the interval [0,2π).​ 15tan⁡3x=5tan⁡x15 \tan ^ { 3 } x = 5 \tan x15tan3x=5tanx ​

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) ​

Find all solutions of the following equation in the interval [0,2π).​ sin⁡3x=sin⁡x\sin ^ { 3 } x = \sin xsin3x=sinx ​

Find all solutions of the following equation in the interval [0,2π).​ sin⁡x−3=cos⁡x−3\sin x - 3 = \cos x - 3sinx−3=cosx−3 ​

Use a graphing utility to graph the function.​ f(x)=2(sin⁡xcos⁡x)f ( x ) = 2 ( \sin x \cos x )f(x)=2(sinxcosx) ​

Find all solutions of the following equation in the interval [0,2π).​ 5sec⁡2x−5=05 \sec ^ { 2 } x - 5 = 05sec2x−5=0 ​

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

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

Use a graphing utility to graph the function.​ f(x)=sin⁡x−cos⁡xf ( x ) = \sin x - \cos xf(x)=sinx−cosx ​

Solve the following equation.​ 2tan⁡23x=62 \tan ^ { 2 } 3 x = 62tan23x=6 ​

Find all solutions of the following equation in the interval [0,2π).​ 3sin⁡x+csc⁡x=03 \sin x + \csc x = 03sinx+cscx=0 ​

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

Sum and Difference Formulas

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

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π). $\csc ^ { 2 } x - 7 \csc x = 0$

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

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

Solve the following equation. $2 \sin ^ { 2 } x = 6 \cos ^ { 2 } x$

Solve the following equation. $\cos ^ { 2 } x + \cos x = 0$

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

Find all solutions of the following equation in the interval [0,2π). $15 \tan ^ { 3 } x = 5 \tan x$

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

Find all solutions of the following equation in the interval [0,2π). $\sin ^ { 3 } x = \sin x$

Find all solutions of the following equation in the interval [0,2π). $\sin x - 3 = \cos x - 3$

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

Find all solutions of the following equation in the interval [0,2π). $5 \sec ^ { 2 } x - 5 = 0$

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

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

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

Solve the following equation. $2 \tan ^ { 2 } 3 x = 6$

Find all solutions of the following equation in the interval [0,2π). $3 \sin x + \csc x = 0$