Exam 5: Trigonometric Functions: Unit Circle Approach

Indicate if the function $f ( x ) = x ^ { 3 } + x \sin ^ { 2 } x$ is even, odd or neither.

Find the exact value of $\operatorname { Sec } \left( \frac { 3 \pi } { 4 } \right)$ and $\csc \left( - \frac { 11 \pi } { 4 } \right)$ .

Find the values of the trigonometric functions of $\text { t }$ given that $\sin t = - \frac { 3 } { 5 }$ and $\cot t < 0$ .

Find the exact value of the expression, if it is defined. $\tan \left( \cos ^ { - 1 } ( \sqrt { 2 } / 2 ) \right)$

Find the period of the function $y = \sec \left( \frac { 1 } { 2 } x - \frac { \pi } { 4 } \right)$ and sketch its graph.

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time $t = 0$ . amplitude 6.25 m, frequency 60 Hz

Find the reference number and the terminal point $P ( x , y )$ determined by $t = - \frac { 7 \pi } { 4 }$ .

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

Graph the three functions $y = - 2 ^ { - x }$ , $y = 2 ^ { - x }$ , and $y = 2 ^ { - x } \sin 4 \pi x$ on a common screen. Explain how the graphs are related.

Find the approximate value of $\sin 2.5$ using a calculator.

Find the period of the function $y = \frac { 1 } { 2 } \csc \left( 2 \left( x + \frac { \pi } { 3 } \right) \right)$ and sketch its graph.

Find $P ( x , y )$ on the unit circle, given that the $x$ - coordinate of $P$ is $\frac { 1 } { 6 }$ and $P$ is in quadrant I.

Each time your heart beats, your blood pressure increases, then decreases as the heart rests between beats. A certain person's blood pressure is modeled by the function $p ( t ) = 120 + 25 \sin ( 150 \pi t )$ , where $p ( t )$ is the pressure in mmHg, at time t measured in minutes. (a) Find the amplitude, average pressure between beats, the maximum and minimum blood pressure, period, and frequency of p. (b) Sketch the graph of p.

An initial amplitude k, damping constant c, and period p are given. a.) Find a function of the form $y = k e ^ { - c t } \sin \omega t$ that models damped harmonic motion. b.) Graph the function. $k = 100 , c = 0.5 , p = \frac { \pi } { 12 }$

Find $P ( x , y )$ on the unit circle, given that the $x$ - coordinate of $P$ is $- \frac { 1 } { 2 }$ and $P$ is in quadrant III.

Find the period of the function $y = \frac { 1 } { 3 } \csc x$ and sketch its graph.

Find the approximate value of $\cos ( - 0.9 )$ using a calculator.

Find the period of the function $y = \frac { 3 } { 2 } \csc \frac { x } { 2 }$ and sketch its graph.

Find the reference number and the terminal point $P ( x , y )$ determined by $t = \frac { 11 \pi } { 6 }$ .

Find the period of the function $y = 3 \sec x$ and sketch its graph.