Exam 5: Trigonometric Functions: Unit Circle Approach

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

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

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

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

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.

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

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

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.

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

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

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

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

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

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

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

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

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

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

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