Exam 2: Acute Angles and Right Triangles

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\frac { \sin 79 ^ { \circ } } { \cos 79 ^ { \circ } }$

Decide whether the statement is true or false. -sec 50° < sec 4°

Use a calculator to decide whether the statement is true or false. -sin (2 ·150°)= 2 · sin 150° · cos 150°

Without using a calculator, give the exact trigonometric function value with rational denominator. -tan 60°

Evaluate. - $2 \tan ^ { 2 } 120 ^ { \circ } + 2 \sin ^ { 2 } 150 ^ { \circ } - \cos ^ { 2 } 0 ^ { \circ }$

Solve the problem. -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.

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 B. He then measures the angle ABC to be 25°36'14''. Estimate the width of the River to the nearest foot. See the figure below.

Determine whether the statement is true or false. -cos(30°+ 45°)= cos 30° · cos 45° - sin 30° · sin 45°

Find a solution for the equation. Assume that all angles are acute angles. -tan(3ϴ + 16°)= cot(ϴ + 4°)

Find a solution for the equation. Assume that all angles are acute angles. - $\sin \left( 2 \beta + 5 ^ { \circ } \right) = \cos \left( 3 \beta - 25 ^ { \circ } \right)$

Solve the problem. -A formula used by an engineer to determine the safe radius of a curve, $R$ , when designing a particular road is: $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$ , 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 $\mathrm { R } = 1229.5 \mathrm { ft }$ , find V. Round to the nearest foot per second.

Determine whether the statement is true or false. - $\cos 300 ^ { \circ } = 1 - \sin ^ { 2 } 150 ^ { \circ }$

Solve the problem. -A boat sails for 2 hours at 30 mph in a direction 95°58'. How far south has it sailed (to the nearest mile)?

Find all values of , if is in the interval [0, 360°) and has the given function value. -cot ϴ = 1

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

Solve the problem. -The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ϴ, where W is the weight of the car and ϴ is the angle of the hill's grade (ϴ > 0 for uphill travel, ϴ < 0 For downhill travel). What is the grade resistance (to the nearest pound)of a 1750-lb car on a level Road (ϴ = 0°)?

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. -sec 70°28´

Find all values of , if is in the interval [0, 360°) and has the given function value. -tan ϴ = 1

Find the exact value of the expression. -cos 45°

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { A } = 11 ^ { \circ } 32 ^ { \prime } , \mathrm { c } = 213 \mathrm { ft }$ Round side lengths to two decimal places.