Deck 5: The Trigonometric Functions

Question 1

The point $( - 8 , - 15 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$ .

Answer 1

$\sin \theta = - \frac { 15 } { 17 }$

Question 2

Use a graphing utility to select the graph of the function
​ $y = \frac { 6 } { x } + \cos x , x > 0$ ​
​

Answer 2

Question 3

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by
​ $v = 0.85 \sin \left( \frac { \pi t } { 2 } \right)$ ,
​
where t is the time (in seconds).
(Inhalation occurs when v > 0 and exhalation occurs when v < 0.)
Select the graph of this velocity function.
​

Answer 3

Question 4

Given the figure below, determine the value of $\sin \theta$ . ​

Question 5

Find (if possible) the complement and supplement of the angle.
​
17°
​

Question 6

Use a graphing utility to select the graph of the function below. Describe the behavior of the function as x approaches 0.
​ $f ( x ) = \frac { 1 - \cos 3 x } { 3 x }$

Question 7

Determine whether the statement is true or false.
​
The Leaning Tower of Pisa is not vertical, but if you know the angle of elevation θ to the top of the tower when you stand 25 feet away from it, you can find its height h using the formula​ $h = 25 \tan \theta$ ​

Question 8

State the period of the function. $$h ( t ) = \cos t$$ ​

Question 9

Use the unit circle below to estimate $\sin 2.0$ to the nearest tenth. ​

Question 10

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window. Describe the behavior of the function as x increases without bound.
​ $f ( x ) = 2 ^ { - \frac { x } { 4 } } \cdot \cos x$

Question 11

The height of an outdoor basketball backboard is $12 \frac { 1 } { 8 }$ feet, and the backboard casts a shadow $17 \frac { 1 } { 5 }$ feet long.
Find the angle of elevation of the sun. Round your answer to one decimal place.
​

Question 12

Find the period and amplitude.
​ $y = - 5 \sin ( x )$ ​

Question 13

Find the relationship between the graphs of f and g. Consider amplitude, period, and shifts.
​ $\begin{array} { l } f ( x ) = \sin ( 9 x ) \\g ( x ) = 2 + \sin ( 9 x )\end{array}$ ​

Question 14

Function g is related to a parent function $f ( x ) = \cos x$ .
​ $g ( x ) = \cos ( 6 x - \pi ) + 4$ ​
Describe the sequence of transformation from f to g.
​

Question 15

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.
​ $$f ( x ) = 9 \cdot 2 ^ { - \frac { x } { 4 } } \cdot \cos ( \pi x )$$ ​