Exam 5: Trigonometric Functions

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 $\theta _ { . }$ - $( 3 , - 6 )$

Evaluate the expression. - $\sec 90 ^ { \circ }$

Solve the problem. -A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed, the angle of depression to the car is $43 ^ { \circ } 15 ^ { \prime }$ . When the car stops, the angle of depression is $27 ^ { \circ } 1 ^ { \prime }$ . The building is 270 feet tall. How far did the car travel from when it was first noticed until it stopped? Round to the nearest foot.

Solve the problem. -A fire is sighted due west of lookout A. The bearing of the fire from lookout $B , 12.0$ miles due south of $A$ , is $N 48 ^ { \circ } 43 ^ { \prime } \mathrm { W }$ . How far is the fire from $B$ (to the nearest tenth of a mile)?

Solve the problem. -To measure the width of a river, a surveyor starts at point A on one bank and walks 74 feet down the river to point $\mathrm { B }$ . He then measures the angle $\mathrm { ABC }$ to be $22 ^ { \circ } 33 ^ { \prime } 111 ^ { \prime \prime }$ . Estimate the width of the river to the nearest foot. See the figure below.

Find the exact value of the expression. - $\cos \left( - 2130 ^ { \circ } \right)$

Solve the problem. -Find the measure of the smaller angle formed by the hands of the clock shown.

Find the angle of least positive measure coterminal with the given angle. - $762 ^ { \circ }$

Find the reference angle for the given angle. - $- 40.0 ^ { \circ }$

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

Evaluate the expression. - $\cot 270 ^ { \circ } + 2 \cos 180 ^ { \circ } + 7 \sec ^ { 2 } 360 ^ { \circ }$

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 $\theta _ { . }$ - $( 3,6 )$

Solve the problem. -A formula used by an engineer to determine the safe radius of a curve, R, when designing a particular road is: $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { g ( \mathrm { f } + \tan \alpha ) }$ , where $\alpha$ is the superelevation of the road and $\mathrm { V }$ is the velocity (in feet per second) for which the curve is designed. If $\alpha = 2.1 ^ { \circ } , \mathrm { f } = 0.1 , \mathrm {~g} = 30$ , and $\mathrm { R } = 1195.11 \mathrm { ft }$ , find V. Round to the nearest foot per second.

Find the exact value of the expression. - $\csc 330 ^ { \circ }$

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 $\theta _ { . }$ - $( 0 , - 5 )$

Solve the problem. -A boat sails for 3 hours at $25 \mathrm { mph }$ in a direction $150 ^ { \circ } 14 ^ { \prime }$ . How far south has it sailed (to the nearest mile)?

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\sin \theta = - \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Decide whether the statement is possible or impossible for an angle θ. - $\sec \theta = - 0.75$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sin 30 ^ { \circ }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\tan 13 ^ { \circ }$