Question 1

Consider the function $$y = 9 \cos \left( 8 x - \frac { \pi } { 3 } \right)$$ . Specify the amplitude.

Accepted Answer

A)  $$18$$ 
B)  $$3$$ 
C)  $$\frac { 9 } { 8 }$$ 
D)  $$9$$ 
E)  $$\frac { 8 } { 9 }$$ 
A)  $$18$$ 
B)  $$3$$ 
C)  $$\frac { 9 } { 8 }$$ 
D)  $$9$$ 
E)  $$\frac { 8 } { 9 }$$

Question 2

Compute $$\sec \alpha$$ , $$\cos \alpha$$ , and $$\sin \alpha$$ . $$\tan \alpha = \frac { 12 } { 5 }$$ and $$\cos \alpha > 0$$

Accepted Answer

A)  $$\sec \alpha = - \frac { 12 } { 13 }$$ , $$\cos \alpha = \frac { 5 } { 13 }$$ , $$\sin \alpha = \frac { 12 } { 13 }$$ 
B)  $$\sec \alpha = \frac { 13 } { 12 }$$ , $$\cos \alpha = \frac { 5 } { 13 }$$ , $$\sin \alpha = \frac { 12 } { 13 }$$ 
C)  $$\sec \alpha = - \frac { 13 } { 5 }$$ , $$\cos \alpha = - \frac { 12 } { 13 }$$ , $$\sin \alpha = \frac { 5 } { 13 }$$ 
D)  $$\sec \alpha = \frac { 5 } { 13 }$$ , $$\cos \alpha = \frac { 13 } { 5 }$$ , $$\sin \alpha = - \frac { 12 } { 13 }$$ 
E)  $$\sec \alpha = \frac { 13 } { 5 }$$ , $$\cos \alpha = \frac { 5 } { 13 }$$ , $$\sin \alpha = \frac { 12 } { 13 }$$ 
A)  $$\sec \alpha = - \frac { 12 } { 13 }$$ , $$\cos \alpha = \frac { 5 } { 13 }$$ , $$\sin \alpha = \frac { 12 } { 13 }$$ 
B)  $$\sec \alpha = \frac { 13 } { 12 }$$ , $$\cos \alpha = \frac { 5 } { 13 }$$ , $$\sin \alpha = \frac { 12 } { 13 }$$ 
C)  $$\sec \alpha = - \frac { 13 } { 5 }$$ , $$\cos \alpha = - \frac { 12 } { 13 }$$ , $$\sin \alpha = \frac { 5 } { 13 }$$ 
D)  $$\sec \alpha = \frac { 5 } { 13 }$$ , $$\cos \alpha = \frac { 13 } { 5 }$$ , $$\sin \alpha = - \frac { 12 } { 13 }$$ 
E)  $$\sec \alpha = \frac { 13 } { 5 }$$ , $$\cos \alpha = \frac { 5 } { 13 }$$ , $$\sin \alpha = \frac { 12 } { 13 }$$

Question 3

Use the Pythagorean identities to simplify the expression. $$\frac { \sec ^ { 2 } \theta - \tan ^ { 2 } \theta } { 1 + \tan ^ { 2 } \theta }$$

Accepted Answer

A)  $$\sec ^ { 2 } \theta$$ 
B)  $$\csc ^ { 2 } \theta$$ 
C)  $$\cos ^ { 2 } \theta$$ 
D)  $$\sin ^ { 2 } \theta$$ 
E)  1 
A)  $$\sec ^ { 2 } \theta$$ 
B)  $$\csc ^ { 2 } \theta$$ 
C)  $$\cos ^ { 2 } \theta$$ 
D)  $$\sin ^ { 2 } \theta$$ 
E)  1

Question 4

Consider the function $$y = 6 + \sin 5 x$$ . Specify the period.

Accepted Answer

A)  $$- \frac { 2 } { 5 } \pi$$ 
B)  $$\frac { 1 } { 6 } \pi$$ 
C)  $$\frac { 1 } { 5 } \pi$$ 
D)  $$\frac { 1 } { 5 }$$ 
E)  $$\frac { 2 } { 5 } \pi$$ 
A)  $$- \frac { 2 } { 5 } \pi$$ 
B)  $$\frac { 1 } { 6 } \pi$$ 
C)  $$\frac { 1 } { 5 } \pi$$ 
D)  $$\frac { 1 } { 5 }$$ 
E)  $$\frac { 2 } { 5 } \pi$$

Question 5

A mass on a smooth tabletop is attached to a spring, as shown in the figure. The coordinate system has been chosen so that the equilibrium position of the mass corresponds to $$s = 0$$ . Assume that the simple harmonic motion is described by the equation $$s = 5 \cos \left( \frac { \pi t } { 3 } \right)$$ , where s is in centimeters and t is in seconds. Determine which table describes the s-coordinate of the mass at each of the following times: $$t =$$ 0 sec, 0.5 sec, 1 sec, and 2 sec. (One of these coordinates will involve a radical sign; for this case, use a calculator and round the final answer to two decimal places.)

Accepted Answer

A)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 5 \
\hline 0.5 & 4.33 \
\hline 1 & 2.5 \
\hline 2 & 2.5 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & - 2.5 \
\hline 0.5 & 4.33 \
\hline 1 & 2.5 \
\hline 2 & 5 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 5 \
\hline 0.5 & 4.33 \
\hline 1 & 2.5 \
\hline 2 & - 2.5 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 2.5 \
\hline 0.5 & 4.33 \
\hline 1 & 5 \
\hline 2 & - 2.5 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 5 \
\hline 0.5 & 2.5 \
\hline 1 & 4.33 \
\hline 2 & - 2.5 \
\hline
\end{array}$$ 
A)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 5 \
\hline 0.5 & 4.33 \
\hline 1 & 2.5 \
\hline 2 & 2.5 \
\hline
\end{array}$$ 
B)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & - 2.5 \
\hline 0.5 & 4.33 \
\hline 1 & 2.5 \
\hline 2 & 5 \
\hline
\end{array}$$ 
C)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 5 \
\hline 0.5 & 4.33 \
\hline 1 & 2.5 \
\hline 2 & - 2.5 \
\hline
\end{array}$$ 
D)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 2.5 \
\hline 0.5 & 4.33 \
\hline 1 & 5 \
\hline 2 & - 2.5 \
\hline
\end{array}$$ 
E)  $$\begin{array} { | c | c | } 
\hline \text { time (sec) } & \text { s-coordinate(cm) } \
\hline 0 & 5 \
\hline 0.5 & 2.5 \
\hline 1 & 4.33 \
\hline 2 & - 2.5 \
\hline
\end{array}$$

Consider the function $y = 9 \cos \left( 8 x - \frac { \pi } { 3 } \right)$ . Specify the amplitude.

Compute $\sec \alpha$ , $\cos \alpha$ , and $\sin \alpha$ . $\tan \alpha = \frac { 12 } { 5 }$ and $\cos \alpha > 0$

Use the Pythagorean identities to simplify the expression. $\frac { \sec ^ { 2 } \theta - \tan ^ { 2 } \theta } { 1 + \tan ^ { 2 } \theta }$

Consider the function $y = 6 + \sin 5 x$ . Specify the period.

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

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Exam 8: Graphs of the Trigonometric Functions

Consider the function y=9cos⁡(8x−π3)y = 9 \cos \left( 8 x - \frac { \pi } { 3 } \right)y=9cos(8x−3π​) . Specify the amplitude.

Compute sec⁡α\sec \alphasecα , cos⁡α\cos \alphacosα , and sin⁡α\sin \alphasinα . tan⁡α=125\tan \alpha = \frac { 12 } { 5 }tanα=512​ and cos⁡α>0\cos \alpha > 0cosα>0

Use the Pythagorean identities to simplify the expression. sec⁡2θ−tan⁡2θ1+tan⁡2θ\frac { \sec ^ { 2 } \theta - \tan ^ { 2 } \theta } { 1 + \tan ^ { 2 } \theta }1+tan2θsec2θ−tan2θ​

Consider the function y=6+sin⁡5xy = 6 + \sin 5 xy=6+sin5x . Specify the period.