Exam 7: Applications of Trigonometric Functions

the motion is simple harmonic with period T, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up.An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that -a = 5; T = 3 seconds A) $\mathrm { d } = - 5 \cos \left( \frac { 1 } { 3 } \pi \mathrm { t } \right)$ B) $d = - 3 \cos \left( \frac { 2 } { 5 } \pi t \right)$ C) $d = - 5 \sin \left( \frac { 2 } { 3 } \pi t \right)$ D) $\mathrm { d } = - 5 \cos \left( \frac { 2 } { 3 } \pi \mathrm { t } \right)$

Use the method of adding y-coordinates to graph the function. - $f ( x ) = x + \cos x$ A) B) C) D)

Find the area of the triangle. If necessary, round the answer to two decimal places. - $\alpha = 20 ^ { \circ } , \mathrm { b } = 13 , \mathrm { c } = 4$

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\cot \mathrm { A }$ when $b = 5$ and $c = 6$ .

Solve the problem. -The distance from home plate to dead center field in a certain baseball stadium is 402 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center Field?

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. - $\mathrm { a } = 14 , \quad \mathrm {~b} = 12 , \quad \beta = 25 ^ { \circ }$

Solve the problem. - $\mathrm { a } = 50 , \mathrm {~b} = 10 , \gamma = 115 ^ { \circ }$

Solve the problem. -It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has the ship sailed from the port? Round your answer to the nearest 0.1 km.

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find $\csc B$ when $a = 9$ and $b = 7$ .

Solve the problem. -A rocket tracking station has two telescopes A and B placed 1.3 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket From telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an Angle of elevation of 27° and telescope B reports an angle of elevation of 52°?

Use the method of adding y-coordinates to graph the function. - $g ( x ) = \sin x - \sin ( 2 x )$ A) B) C) D)

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find sin B when b = 4 and c = 7. A) $\frac { 4 } { 7 }$ B) $\frac { \sqrt { 33 } } { 7 }$ C) $\frac { 4 \sqrt { 33 } } { 33 }$ D) $\frac { 7 \sqrt { 33 } } { 33 }$

Solve the problem. -A surveyor standing 56 meters from the base of a building measures the angle to the top of the building and finds it to be 39°. The surveyor then measures the angle to the top of the radio tower on the building and finds That it is 49°. How tall is the radio tower?

Solve the problem. -Two surveyors 180 meters apart on the same side of a river measure their respective angles to a point between them on the other side of the river and obtain 54° and 68°. How far from the point (line-of-sight distance) is each surveyor? Round your answer to the nearest 0.1 meter.

Solve the problem. -A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest Hundredth of a meter?

Solve the triangle. Find the angles α and β first. -

Find the area of the triangle. If necessary, round the answer to two decimal places. -a = 14, b = 32, c = 26

Solve the problem. -A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing S52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420 Mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile.

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give exact answers with rational denominators. -Find sin A when a = 8 and b = 7. A) $\frac { \sqrt { 113 } } { 7 }$ B) $\frac { \sqrt { 113 } } { 8 }$ C) $\frac { 8 \sqrt { 113 } } { 113 }$ D) $\frac { 7 \sqrt { 113 } } { 113 }$

Solve the problem. - $a = 6 , b = 8 , \gamma = 70 ^ { \circ }$