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 = 10 seconds A) $d = 5 \cos ( 10 t )$ B) $d = - 5 \cos ( 10 t )$ $C ) d = - 5 \cos \left( \frac { \pi } { 5 } t \right)$ D) $\mathrm { d } = 5 \cos \left( \frac { \pi } { 5 } \mathrm { t } \right)$

Solve the problem. -Find $\tan P$ .

Solve the problem. - $\cos 35 ^ { \circ } \sin 55 ^ { \circ } + \sin 35 ^ { \circ } \cos 55 ^ { \circ }$

Solve the triangle. - $\beta = 10 ^ { \circ } , \quad \gamma = 100 ^ { \circ } , \quad \mathrm { a } = 4$

Solve the problem. -A building 200 feet tall casts a 40 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest Degree)? (Assume the person's eyes are level with the top of the building.)

Find the area of the triangle. If necessary, round the answer to two decimal places. - $\alpha = 83 ^ { \circ } , b = 9 , c = 6$

The displacement d (in meters) of an object at time t (in seconds) is given. Describe the motion of the object. What is the maximum displacement from its resting position, the time required for one oscillation, and the frequency? - $d = - 1 \cos \left( \frac { \pi } { 2 } t \right)$

Solve the problem. -Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B? Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning Angle.)

Find the area of the triangle. If necessary, round the answer to two decimal places. -

Solve the problem. -John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the angle of elevation from where he is looking as 35°. He walks 30 feet closer to the tree and finds That the angle of elevation has increased by 12°. Estimate the height of the tree rounded to the nearest whole Number.

Solve the problem. - $\tan 15 ^ { \circ } - \frac { \cos 75 ^ { \circ } } { \cos 15 ^ { \circ } }$

Find the area of the triangle. If necessary, round the answer to two decimal places. -a = 4, b = 5, c = 7

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 cos A when a = 3 and b = 7. A) $\frac { \sqrt { 58 } } { 7 }$ В) $\frac { 7 \sqrt { 58 } } { 58 }$ C) $\frac { 3 \sqrt { 58 } } { 58 }$ D) $\frac { \sqrt { 58 } } { 3 }$

Solve the problem. -

Solve the problem. -In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at 0.314 arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about 150,000,000 km and $\theta = 0.314 \text { seconds } = \frac { 0.314 } { 60 } \text { minutes } = \frac { 0.314 } { 60 \cdot 60 } \text { degrees }$ determine the distance d from Earth to 61 Cygni using Bessel's figures.

Solve the problem. -A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down the shoreline from the pier and measures the angle formed by the ends of the pier. If is found to be 53°. What acute angle (correct to the nearest 0.1°) does the pier form with the shoreline? Is there more than one possibility? If so, how can we know which is the correct one?

Graph the damped vibration curve for 0 $0 \leq t \leq 2 \pi$ . - $d ( t ) = e ^ { - t / 2 \pi } \cos ( 2 t )$ A) B)

Solve the problem. -A box has dimensions 2" × $3 "$ × 4". (See illustration.) Determine the angle $\theta$ formed by the diagonal of the $2 " \times 3 "$ side and the diagonal of the $3 " \times 4$ " side. Round your answer to the nearest degree.

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 sec $B$ when $a = 9$ and $b = 5$ .

Graph the damped vibration curve for 0 $0 \leq t \leq 2 \pi$ . -The distance d (in meters) of the bob of a pendulum from its rest position at time t (in seconds) is given by: $d = - 9 e ^ { - 0.6 t } / 60 \cos \left( \sqrt { \left( \frac { 2 \pi } { 7 } \right) ^ { 2 } - \frac { 0.36 } { 3600 } } t \right)$ What is the maximum displacement of the bob after the first oscillation?