Question 1

Find y by referring to the graph of the trigonometric function. $\text { As } \quad x \rightarrow 0 ^ { - } , \csc x \rightarrow y$

Accepted Answer

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

Question 2

Sketch the graph of the equation. $y = x + \sin x$

Accepted Answer

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

Question 3

Let P ( t ) be the point on the unit circle U that corresponds to t. If P ( t ) has the coordinates $\left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ , find $P ( t + \pi )$ , $P ( t - \pi )$ , $P ( - t )$ , $P ( - t - \pi )$ .

Accepted Answer

A)  $P ( t + \pi ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
B)  $P ( t + \pi ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
C)  $P ( t + \pi ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
D)  $P ( t + \pi ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
E)  $P ( t + \pi ) = \left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
A)  $P ( t + \pi ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
B)  $P ( t + \pi ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
C)  $P ( t + \pi ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
D)  $P ( t + \pi ) = \left( - \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ 
E)  $P ( t + \pi ) = \left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right) , P ( \pi - t ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ $P ( - t ) = \left( \frac { 21 } { 29 } , - \frac { 20 } { 29 } \right) , P ( - t - \pi ) = \left( - \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$

Question 4

On March 17, 1981, in Tucson, Arizona, the temperature in degrees Fahrenheit could be described by the equation $T ( t ) = - 10 \cos \left( \frac { \pi } { 12 } t \right) + 55$ while the relative humidity in percent could be expressed by $H ( t ) = 25 \cos \left( \frac { \pi } { 12 } t \right) + 60$ where t is in hours and t = 0 corresponds to 6 AM. Find the maximum value of the humidity.

Accepted Answer

A)  H = 10% 
B)  H = 90% 
C)  H = 35% 
D)  H = 55% 
E)  H = 85% 
A)  H = 10% 
B)  H = 90% 
C)  H = 35% 
D)  H = 55% 
E)  H = 85%

Question 5

Use fundamental identities to find the exact values of the trigonometric functions for the given conditions. $\csc \theta = 7 \text { and } \cot \theta < 0$

Accepted Answer

A)  $\begin{array} { l } 
\sin \theta = - \frac { \sqrt { 48 } } { 7 } , \quad \cos \theta = \frac { 1 } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 7
\end{array}$ 
B)  $\begin{array} { l } 
\sin \theta = - \frac { 1 } { 7 } , \quad \cos \theta = \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = \frac { 1 } { \sqrt { 48 } } \
\cot \theta = \sqrt { 48 } , \quad \sec \theta = \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = - 7
\end{array}$ 
C)  $\begin{array} { c c } 
\sin \theta = \frac { 1 } { 48 } , \quad \cos \theta = - \frac { \sqrt { 48 } } { 48 } , \quad \tan \theta = - 1 \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 48
\end{array}$ 
D)  $\begin{array} { c } 
\sin \theta = \frac { 1 } { 7 } , \quad \cos \theta = - \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 7
\end{array}$ 
E)  $\begin{array} { l } 
\sin \theta = - \frac { 1 } { 48 } , \quad \cos \theta = \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 48 } { \sqrt { 48 } } , \quad \csc \theta = - 7
\end{array}$ 
A)  $\begin{array} { l } 
\sin \theta = - \frac { \sqrt { 48 } } { 7 } , \quad \cos \theta = \frac { 1 } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 7
\end{array}$ 
B)  $\begin{array} { l } 
\sin \theta = - \frac { 1 } { 7 } , \quad \cos \theta = \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = \frac { 1 } { \sqrt { 48 } } \
\cot \theta = \sqrt { 48 } , \quad \sec \theta = \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = - 7
\end{array}$ 
C)  $\begin{array} { c c } 
\sin \theta = \frac { 1 } { 48 } , \quad \cos \theta = - \frac { \sqrt { 48 } } { 48 } , \quad \tan \theta = - 1 \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 48
\end{array}$ 
D)  $\begin{array} { c } 
\sin \theta = \frac { 1 } { 7 } , \quad \cos \theta = - \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 7 } { \sqrt { 48 } } , \quad \csc \theta = 7
\end{array}$ 
E)  $\begin{array} { l } 
\sin \theta = - \frac { 1 } { 48 } , \quad \cos \theta = \frac { \sqrt { 48 } } { 7 } , \quad \tan \theta = - \frac { 1 } { \sqrt { 48 } } \
\cot \theta = - \sqrt { 48 } , \quad \sec \theta = - \frac { 48 } { \sqrt { 48 } } , \quad \csc \theta = - 7
\end{array}$

Find y by referring to the graph of the trigonometric function. $\text { As } \quad x \rightarrow 0 ^ { - } , \csc x \rightarrow y$

Sketch the graph of the equation. $y = x + \sin x$

Let P ( t ) be the point on the unit circle U that corresponds to t. If P ( t ) has the coordinates $\left( \frac { 21 } { 29 } , \frac { 20 } { 29 } \right)$ , find $P ( t + \pi )$ , $P ( t - \pi )$ , $P ( - t )$ , $P ( - t - \pi )$ .

Use fundamental identities to find the exact values of the trigonometric functions for the given conditions. $\csc \theta = 7 \text { and } \cot \theta < 0$

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Applications of Trigonometry

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Exam 5: Trigonometric Functions

Find y by referring to the graph of the trigonometric function. As x→0−,csc⁡x→y\text { As } \quad x \rightarrow 0 ^ { - } , \csc x \rightarrow y As x→0−,cscx→y

Sketch the graph of the equation. y=x+sin⁡xy = x + \sin xy=x+sinx

Use fundamental identities to find the exact values of the trigonometric functions for the given conditions. csc⁡θ=7 and cot⁡θ<0\csc \theta = 7 \text { and } \cot \theta < 0cscθ=7 and cotθ<0

Topics From Algebra

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series, and Probability

Topics From Analytical Geometry

Filters

Find y by referring to the graph of the trigonometric function. $\text { As } \quad x \rightarrow 0 ^ { - } , \csc x \rightarrow y$

Sketch the graph of the equation. $y = x + \sin x$

Use fundamental identities to find the exact values of the trigonometric functions for the given conditions. $\csc \theta = 7 \text { and } \cot \theta < 0$