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Exam 5: Trigonometric Functions: Unit Circle Approach

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Question 51

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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.

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is a sine function that lies ...

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Question 52

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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

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Question 53

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

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

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

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.

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

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

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

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

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.

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

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

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

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

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

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

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