Exam 6: Trigonometric Functions

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -Any offset between a stationary radar gun and a moving target creates a "cosine effect" that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the radar speed Reading is the product of the actual reading and the cosine of the angle. Find the radar reading to the Nearest hundredth for the auto shown in the figure.

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the given point is on the terminal side of $\theta$ (3, 6) -

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\sin \theta = 6.94$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\cos 60 ^ { \circ }$

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\cot \theta = - \frac { 9 } { 8 }$ and $\cos \theta < 0$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $115 ^ { \circ }$

Perform the calculation. - $90 ^ { \circ } - 19 ^ { \circ } 39 ^ { \prime }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -If an automobile is traveling at velocity $\mathrm { V }$ (in feet per second), the safe radius $\mathrm { R }$ for a curve with superelevation $\alpha$ is given by the formula $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$ , where $\mathrm { f }$ and $\mathrm { g }$ are constants. A road is being constructed for automobiles traveling at 49 miles per hour. If $\alpha = 4 ^ { \circ } , \mathrm { g } = 31.6$ , and $\mathrm { f } = 0.16$ , calculate $R$ . Round to the nearest foot. (Hint: 1 mile $= 5280$ feet)

Solve the problem. -A wheel is rotating 600 times per minute. Through how many degrees does a point on the edge of the wheel move in $\frac { 1 } { 2 }$ seconds?

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $a = 3.5 \mathrm {~m} , \mathrm {~B} = 21.8 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Find the exact value of the expression. - $\cot \left( - 1215 ^ { \circ } \right)$

Solve the problem. -A boat sails for 3 hours at $35 \mathrm { mph }$ in a direction $122 ^ { \circ } 31 ^ { \prime }$ . How far south has it sailed (to the nearest mile)?

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $170 ^ { \circ }$

Solve the problem. -An airplane travels at $185 \mathrm {~km} / \mathrm { h }$ for $5 \mathrm { hr }$ in a direction of $112 ^ { \circ }$ from a local airport. At the end of this time, how far east of the airport is the plane (to the nearest kilometer)?

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\tan \theta = - \frac { 4 } { 9 }$ and $\theta$ is in quadrant II.

Evaluate the expression. - $\cos 360 ^ { \circ } - 8 \sin 90 ^ { \circ }$

The number represents an approximate measurement. State the range represented by the measurement. -12 ft

Perform the calculation. - $177 ^ { \circ } 35 ^ { \prime } + 12 ^ { \circ } 53 ^ { \prime }$

Solve the problem. -In one area, the lowest angle of elevation of the sun in winter is $25 ^ { \circ } 1 ^ { \prime }$ . A fence is to be built $13.3 \mathrm { ft }$ away from a plant in the direction of the sun. (See drawing) Find the maximum height, $x$ , for the fence so that the plant will get full sun. Round your answer to the tenths place when necessary.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\frac { 1 } { \tan 46 ^ { \circ } 31 ^ { \prime } }$