Exam 5: Trigonometric Functions

Solve the problem. -Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be $23 ^ { \circ } 17 ^ { \prime }$ . He then drives 1 mile $\left( 1 \mathrm { mile } = 5280 \mathrm { ft } \right.$ ) more and measures the angle of elevation to be $34 ^ { \circ } 32 ^ { \prime }$ . Find the height of the mountain to the nearest foot.

Solve the problem. -Find $h$ as indicated in the figure. Round to the nearest foot.

Solve the problem. -The grade resistance $F$ of a car traveling up or down a hill is modeled by the equation $F = W \sin \theta$ , where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). What is the grade resistance (to the nearest pound) of a $1000 - \mathrm { lb }$ car traveling uphill on a $1 ^ { \circ } \operatorname { grade } \left( \theta = 1 ^ { \circ } \right)$ ?

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

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. - $10 ^ { \circ }$

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\cos \theta = \frac { 1 } { 2 }$

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\cos \theta = \frac { \sqrt { 3 } } { 2 }$

Solve the problem. -Find a formula for the area of the figure in terms of s.

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 $\theta _ { . }$ - $( - 5,3 )$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sec 21 ^ { \circ } 19 ^ { \prime }$

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 4 , - 7 )$ ; Find $\tan \theta$

If n is an integer, n ∙ 180° represents an integer multiple of 180°, and (2n + 1) ∙ 90° represents an odd integer multiple of 90°. Decide whether the expression is equal to 0, 1, -1, or is undefined. - $\tan \left( \mathrm { n } \cdot 180 ^ { \circ } \right)$

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. - $20 ^ { \circ }$

Solve the problem. -A tunnel is to be dug from point $A$ to point $B$ . Both $A$ and $B$ are visible from point $C$ . If $A C$ is 160 miles and $\mathrm { BC }$ is 349 miles, and if angle $\mathrm { C }$ is $90 ^ { \circ }$ , find the measure of angle $\mathrm { B }$ . Round your answer to the tenths place.

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 $\mathrm { a } = 5$ and $\mathrm { c } = 6$ .

Find the measure of each angle in the problem. -

Find the measure of each angle in the problem. -Supplementary angles with measures 2x + 6 and 3x - 1 degrees

Find the exact value of the expression. - $\sec 150 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\csc 7 ^ { \circ } 34 ^ { \prime }$

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sec \theta = - \sqrt { 2 }$