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Exam 5: Trigonometric Functions: Unit Circle Approach

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Question 31

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Find the value of $\sin ^ { - 1 } \left( \sin \frac { \pi } { 15 } \right)$ if it is defined.

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Question 32

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Find the value of $\cos ^ { - 1 } \left( \cos \frac { 12 \pi } { 13 } \right)$ if it is defined.

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Question 33

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The function $y = 5 \cos \left( 1.5 t - \frac { \pi } { 3 } \right)$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the amplitude, period, and frequency of motion and sketch a graph of the function over one complete period.

Sketch the graph of $y = - 2 \cos x$ .

Find the value of $\cos \left( \cos ^ { - 1 } ( - 13 ) \right)$ if it is defined.

Find the terminal point $P ( x , y )$ on the unit circle determined by the value $t = - \frac { 3 \pi } { 4 }$ .

Find the approximate value of $\tan ( 1.5 )$ using a calculator.

On the unit circle, determine which quadrant contains the terminal point of the arc whose length is $- 1.56$ .

Find the reference number and the terminal point $P ( x , y )$ determined by .

The function $y = 1.6 \sin ( t - 1.8 )$ models the displacement of an object moving in simple harmonic motion, where y is measured in inches and t in seconds. Find the amplitude, period, and frequency of motion and sketch a graph of the function over one complete period.

Find the period of the function $y = \sec 7 x$ and sketch its graph.

Find a function that models the simple harmonic motion having the given properties. Sketch its graph. Assume that the displacement is at its maximum at time $t = 0$ . amplitude 35 cm, period 8 seconds

Find the value of $\sin ^ { - 1 } \left( - \frac { 1 } { 2 } \right)$ if it is defined.

Sketch the graph of $y = \frac { 1 } { 2 } + \frac { 1 } { 2 } \cos x$ .

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time t. amplitude 1.2 cm, frequency 0.5 Hz

Sketch the graph of $y = 2 - \sin x$ .

Find the amplitude, period and phase shift of $y = - 2 \sin \left( 2 x - \frac { 3 } { 2 } \right)$ and sketch its graph.

Find the value of $\tan \left( \tan ^ { - 1 } 169 \right)$ if it is defined.

Sketch the graph of $y = 2 - \cos x$ .

Find the amplitude, period, and phase shift of the function $y = 2 \cos \left( \frac { 1 } { 4 } x + \frac { 1 } { 2 } \pi \right)$ , and sketch its graph for one complete period.