Exam 4: Trigonometric Functions

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - $f ( x ) = 9 \arccos \left( \frac { x } { 7 } \right)$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\cos 540 ^ { \circ }$

Find the amplitude of the function. - $y = 5 \sin \frac { 1 } { 4 } x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\csc \frac { 4 \pi } { 3 }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -136°54'53"

Select the functions that have identical graphs. -(i) $y = \cos x$ (ii) $y = \cos \left( x - \frac { 5 \pi } { 2 } \right)$ (iii) $y = \sin x$

Use the arc length formula and the given information to find the indicated quantity. - $\mathrm { s } = 3.4 \mathrm { ft } , \theta = \frac { \pi } { 3 } \mathrm { rad } ;$ find $\mathrm { r }$

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

Find the domain and range of the function. - $f ( x ) = - 9 \cot ^ { 2 } x$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = 2 \cos 3 \pi x ; g ( x ) = \cos \pi x$

Find the zeros of the function in the interval $[-2 \pi, 2 \pi]$ . - $f ( x ) = - 4 \sin x$

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 3 , period 8 , point $( 7,0 )$

Use a calculator to find the function value to four decimal places. - $\sin 34 ^ { \circ } 43 ^ { \prime } 3 ^ { \prime \prime }$

Solve the problem. -Tides go up and down in a 14.4-hour period. The average depth of a certain river is $15 \mathrm {~m}$ and ranges from 10 to $20 \mathrm {~m}$ . 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 if high tide occurs at $6 : 00$ am.

Find the angle $\theta$ (if it exists) in the interval $\left[ 0 ^ { \circ } , 90 ^ { \circ } \right.$ ) for which $\tan \theta = \cot \theta$ .

Solve. -In the study of alternating electric current, capacitive voltage is given by $V c = - \frac { i } { 2 \pi f } \cos 2 \pi f t$ , where $f$ is the number of cycles per second, $\mathrm { i }$ is the maximum current, and $\mathrm { t }$ is the time in seconds. Solve the equation for t.

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \sin \left( x + \frac { \pi } { 2 } \right) ; g ( x ) = \sin \left( x + \frac { \pi } { 3 } \right)$

Find the angle in degrees that describes the compass bearing. -ESE

Solve the problem. -Suppose that the average monthly low temperatures for a small town are shown in the table. Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$ .

Give the exact value. - $\cos \frac { \pi } { 4 }$