Exam 6: Trigonometric Functions

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ - $( - 3 , - 2 ) ;$ Find $\tan \theta$

Find the measure of each angle in the problem. -

Find the exact value of the expression. - $\tan \theta = 1$

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { \sqrt { 3 } } { 2 }$ .

Provide an appropriate response. -Find the supplement of an angle whose measure is 117°. 3)

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

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the shadow is 40 meters, how tall is the flag pole?

Evaluate the expression. - $\cot 90 ^ { \circ } + 2 \cos 180 ^ { \circ } + 4 \sec ^ { 2 } 360 ^ { \circ }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $5 ^ { \circ } 20 ^ { \prime } 38 ^ { \prime \prime }$

An equation of the terminal side of an angle $\theta$ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of $\theta$ . Do not use a calculator. - $- 3 x - 5 y = 0 , \quad x \geq 0 ; \quad$ Find $\cos \theta$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\cos 183 ^ { \circ } 55 ^ { \prime }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\cos 64 ^ { \circ }$

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. - $50 ^ { \circ }$

Provide an appropriate response. -Find the supplement of an angle whose measure is $37 ^ { \circ } 51 ^ { \prime } 5 ^ { \prime \prime }$

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. - $130 ^ { \circ }$

Evaluate the expression. - $\cos \left( - 180 ^ { \circ } \right)$

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. -Find $\cot \mathrm { A }$ when $\mathrm { a } = 9$ and $\mathrm { c } = 10$ .

The number represents an approximate measurement. State the range represented by the measurement. -69.62 k

Solve the right triangle. If two sides are given, give angles in degrees and minutes. -To measure the width of a river, a surveyor starts at point $\mathrm { A }$ on one bank and walks 72 feet down the river to point $\mathrm { B }$ . He then measures the angle $\mathrm { ABC }$ to be $22 ^ { \circ } 36 ^ { \prime } 10 ^ { \prime \prime }$ . Estimate the width of the rive to the nearest foot. See the figure below.

Solve the problem. -A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed, the angle of depression to the car is $28 ^ { \circ } 17 ^ { \prime }$ . When the car stops, the angle of depression is $44 ^ { \circ } 59 ^ { \prime }$ . The building is 210 feet tall. How far did the car travel from when it was first noticed until it stopped? Round to the nearest foot.