Exam 4: Graphs of the Circular Functions

Match the function with its graph. -1) $y = - \csc x$ 2) $y = - \sec x$ 3) $y = - \tan x$ 4) $y = - \cot x$ a) b) c) d)

Graph the function. - $y=\frac{2}{3} \sin \left(x+\frac{\pi}{2}\right)$

Use Identities to find the exact value. -Tides go up and down in a 14.8-hour period. The average depth of a certain river is 7 m and ranges from 4 to 10 m. The variation can be approximated by a sine curve. Write an equation that gives the Approximate variation y, if x is the number of hours after midnight and high tide occurs at 5:00 am.

Graph the function. - $y=\frac{2}{5} \sec \left(\frac{1}{2} x-\frac{\pi}{4}\right)$

Give the amplitude or period as requested. -Period of y = sin 3x

Find the phase shift of the function. - $y = - 3 \cos ( 4 x + \pi )$

Solve the problem. -The voltage E in an electrical circuit is given by E = 1.3 cos 100πt, where t is time measured in seconds. Find the period.

Solve the problem. -A weight attached to a spring is pulled down 8 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ second.

Graph the function. - $y=\sin \pi x$

Find the phase shift of the function. - $y = - 3 - 2 \sin \left( 4 x - \frac { \pi } { 3 } \right)$

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Graph the function. - $y=-2+\sin \left(x+\frac{\pi}{2}\right)$

Graph the function. - $y = \frac { 1 } { 2 } \tan x$

Find the specified quantity. -Find the period of $y = 3 \cos \left( 3 x + \frac { \pi } { 2 } \right)$ .

Give the amplitude or period as requested. -Amplitude of $y = \cos \frac { 1 } { 3 } x$

Solve the problem. -The temperature in Fairbanks is approximated by $T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25$ where $\mathrm { T } ( \mathrm { x } )$ is the temperature on day $x$ , with $x = 1$ corresponding to Jan. 1 and $x = 365$ corresponding to Dec. 31. Estimate the temperature on day 49 .

Find the phase shift of the function. - $y = - 2 \sin \left( x - \frac { \pi } { 4 } \right)$

Find the specified quantity. -Find the amplitude of $y = - 4 \sin ( 2 x + \pi )$ .

Find the phase shift of the function. - $y = \sin \left( x + \frac { \pi } { 4 } \right)$

Match the function with its graph. -1) $y = \tan x$ 2) $y = \cot x$ 3) $y = - \tan x$ 4) $y = - \cot x$ a) b) c) d)