Exam 6: Trigonometric Functions: Unit Circle Approach

To find the distance across a river a surveyor chooses points $A$ and $B$ , $50$ M apart and a reference point $C$ On the opposite side of theriver. Approximate the distance, $b$ , between $A$ And $C$ Given that $\angle \mathrm { A } =54 ^ { \circ }$ And $\angle B = 77 ^ { \circ }$

Use Heron's formula to find the area of the triangle with sides of length 10, 12, and 20.

Find the area of a sector with central angle $3 \pi / 2$ in a circle with radius $5$ m.

Find the area of a triangle with sides of length 12 and 22 and included angle $12 ^ { \circ }$ .

Find the angle $\theta$ in the triangle. Round the answer to one decimal place.

Find the exact value of the expression. $\left( \sin 30 ^ { \circ } \right) ^ { 2 } - \left( \cos 30 ^ { \circ } \right) ^ { 2 }$

Find the angle $\theta$ in the triangle. Round the answer to one decimal place.

Find the degree measure that corresponds to each radian measure. $\frac { 3 \pi } { 5 }$ , $\frac { 11 \pi } { 6 }$

Find $\sin \theta$ and $\cot \theta$ Given that $\sec \theta = - 2$ And $\tan \theta > 0$

Rewrite the expression as an algebraic expression in x. $\tan \left( \sin ^ { - 1 } x \right)$

From the top of a $250$ ft lighthouse, the angle of depression to a ship in the ocean is $18 ^ { \circ }$ . How far is the ship from the base of the lighthouse?

A plane leaves the airport at 4:00 p.m. and heads in the direction N $10 ^ { \circ }$ E at a constant speed of $250$ mi/h. Forty-five minutes later, a jet leaves the same airport and flies N $60 ^ { \circ }$ W at a constant speed of $450$ mi/h. Find the distance between the plane and the jet at 5:30p.m.

Find the acute angle that is formed by the line $y - x + 1 = 0$ and the x-axis.

Find the radian measure that corresponds to each degree measure. a) $315 ^ { \circ }$ b) $- 225 ^ { \circ }$

A $200$ ft guy wire is attached to the top of a tower. If the wire makes a $55 ^ { \circ }$ Angle with the ground, how tall is the tower?

Find $\tan \theta$ and $\cot \theta$

Find the degree measures that correspond to the radian measures $\pi / 5$ and $3.1$ . Write your answer(s) to one decimal place.

Find all angles $\theta$ between $0$ and $180 ^ { \circ }$ satisfying the given equation. Round all answers to two decimal places. $\sin \theta = 1 / 8$

Find the exact value of the expression. $\sec \left( \sin ^ { - 1 } \frac { 5 } { 13 } \right)$

A pilot sets out from an airport and heads in the direction N $30 ^ { \circ }$ W, flying at a constant speed of $305$ mi/h. Forty-five minutes later the pilot makes a course and speed correction and now heads in the direction N $50 ^ { \circ }$ W and reduces her speed to $175$ mi/h. Half an hour later, engine trouble forces her to make an emergency landing. Find the distance between the airport and the final landing point