## [answered] Midterm Exam - FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC

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Midterm Exam - FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY

University of Maryland University College

FALL 2016, MATH 108

Midterm Exam

Prof. Minhtri Ho The midterm exam has 20 problems with each problem being worth 5 points.

The total score of the midterm exam is 100 points and it counts for 16% of the final grade

of the class.

Please submit the midterm exam by 11:59 PM Eastern Time November 20, 2016.

Problem 1:

Let ? = 71.389? , and ? = 42? 560 4100 .

a) Convert ? to the DMS system. Round your answer to the nearest second.

b) Convert ? to decimal degrees. Round your answer to the nearest thousandth of a

degree.

Problem 2:

A yo-yo which is 2.5 inches in diameter spins at a rate of 5000 revolutions per minute.

How fast is the edge of the yo-yo spinning in miles per hour? Round your answer to two

decimal places.

Problem 3:

Imagine a rope tied around the Earth at the equator. Show that you need to add only

2? feet of length to the rope in order to lift it one foot above the ground around the entire

equator. (You do NOT need to know the radius of the Earth to show this.)

Problem 4:

If ? is a Quadrant II angle with cos(?) = ? 23 , find sin(?). FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY Midterm Exam - FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY Problem 5:

Find the measure of the missing angle and the lengths of the missing sides of: Problem 6:

Find the exact value of cos(15? )

Problem 7: [Hint: Be careful, this could be a trick question! ]

Find the exact value of the following:

arccos(?2)

Problem 8:

Solve the following equation:

arccos(3x) = ?

3 Problem 9:

Solve the following inequality on [0, 2?)

tan(x) ? 1

FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY Midterm Exam - FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY Problem 10:

Solve the equation, giving the exact solutions which lie in [0, 2?)

sin(2x) = sin(x)

Problem 11:

Solve the inequality. Express the exact answer in interval notation, restricting your

attention to 0 ? x &lt; 2?

sin2 (x) &gt; 1

2 Problem 12:

?

Write x(t) = (t + 1) 3 cos(2t) + (t + 1) sin(2t) in the form x(t) = A(t) sin(?t + ?). Graph

x(t) using a graphing utility.

Problem 13:

Write x(t) = 2e?t/6 cos(t) + 2e?t/6 sin(t) in the form x(t) = A(t) sin(?t + ?). Graph x(t)

using a graphing utility.

Problem 14:

Suppose an object weighing 64 pounds stretches a spring 8 feet. If the object is attached

to the spring and released 5 feet below the equilibrium position from rest, find the equation

of motion of the object, x(t).

Problem 15:

?

The voltage V in an alternating current source has amplitude 110 2 and ordinary frequency f = 50 Hertz. Find a sinusoid which models this voltage. Assume that the phase is

?/2. FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY Midterm Exam - FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY Problem 16:

Solve the following triangle. Give exact answers and decimal approximations (rounded

to hundredths) and sketch the triangle.

? = 120? , a = 9 units, ? = 30?

Problem 17: [Hint: Be careful, this could be a trick question! ]

Solve the following triangle. Give exact answers and decimal approximations (rounded

to hundredths) and sketch the triangle.

? = 120? , a = 2 units, c = 4 units

Problem 18:

Find the area of the triangle given by:

? = 45? , a = 25, b = 5

Use a scientific calculator for trigonometric values.

Problem 19:

The hour hand on my antique Seth Thomas schoolhouse clock in 4 inches long and the

minute hand is 5.5 inches long. Find the distance between the ends of the hands when the

Problem 20:

A geologist wants to measure the diameter of a crater. From her camp, it is 8 miles to

the northern-most point of the crater and 4 miles to the southern-most point. If the angle

between the two lines of sight is 117? , what is the diameter of the crater? Round your answer

to the nearest hundredth of a mile. FALL 2016 - MATH 108 - TRIGONOMETRY ANALYTIC GEOMETRY

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