Precal Quiz

QUIZ 4 Professor: Ms. Chowdhury MATH 115 Fall 2018 Name___________________________________ Date ________________ INSTRUCTIONS

The quiz is worth 55 points. There are 20 multiple choice (2 points) and 5 (3 points) short answer problems.

This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.

You must show all of your work for the short answers to receive full credit. If you do not show work, you may earn only partial or no credit at the discretion of the professor. Work for multiple choice is not mandatory, but highly encouraged.

Please type your answers on the table in the answer sheet provided, then create a separate document containing your work. Scanned handwritten work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module.

If you have any questions, please contact me by e-mail.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

0 t < 2

and sin t is given. Use the Pythagorean identity sin2 t + cos2 t = 1 to find cos t.

1) sin t = 14

A) 4 15 15

B) 4 C) 15 4

D) 15 15

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function of .

2) (4, -2) Find sin .

A) - 5 5

B) -2 C) 2 5 5

D) 5 2

3) (-5, 9) Find cot .

A) - 1 2 B) -

9 5 C) -

5 9 D)

9 10

1

Complete the identity.

4) csc x(sin x + cos x) = ?

A) -2 tan2 x B) sec x csc x C) 1 + cot x D) sin x tan x

Find a cofunction with the same value as the given expression.

5) sin 61°

A) cot 29° B) cos 29° C) tan 29° D) cos 61°

Find an equation for the graph.

6)

A) y = 3 cos 2x B) y = 2 cos 3x C) y = 2 cos 13 x D) y = 3 cos 12

x

Find the exact value by using a sum or difference identity.

7) sin 165°

A) 2( 3 + 1) 4

B) - 2( 3 - 1) 4

C) - 2( 3 + 1) 4

D) 2( 3 - 1) 4

Find the exact value of the expression if = 45°. Do not use a calculator.

8) (cos )2

A) 12 B) 2 C) 2 D) - 2

2

Find the exact value of the expression.

9) cos 10° cos 50° - sin 10° sin 50°

A) 3 B) 12 C) 1 4 D)

3 2

Find the reference angle for the given angle.

10) -418°

A) 32° B) 148° C) 58° D) 122°

2

Provide an appropriate response.

11) State the range of the inverse tangent function.

A) [-1, 1] B) - 2 ,

2 C) 2 , -

2 D) (- , )

Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators.

12) sin t = - 2 7 , cos t =

-3 5 7

. Find tan t.

A) 2 5 15

B) - 7 2 C)

-7 5 15

D) 2 5 2

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest tenth of a degree.

13) A = 35°, b = 43.9

A) B = 55°, a = 62.7, c = 76.5 B) B = 35°, a = 36, c = 30.7

C) B = 55°, a = 30.7, c = 53.6 D) B = 35°, a = 62.7, c = 36

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given angle. Give an exact answer with a rational denominator.

14)

4

5 Find csc .

A) csc = 4 41 41

B) csc = 41 5

C) csc = 5 41 41

D) csc = 41 4

Use a calculator to find the value of the expression rounded to two decimal places.

15) sin-1 6 5

A) 1.06 B) 60.67 C) 29.33 D) 0.51

Use a calculator to find the value of the trigonometric function to four decimal places.

16) cos 0.7

A) 0.9999 B) 0.7648 C) 0.6442 D) 0.0122

3

17) cot 0.1884

A) 5.2449 B) 0.9823 C) 0.1907 D) 1.0180

Use an identity to find the value of the expression. Do not use a calculator.

18) sin2 4 + cos2

4

A) 4 B) -

4 C) -1 D) 1

Use even and odd properties of the trigonometric functions to find the exact value of the expression.

19) tan (- 6 )

A) - 3 3

B) - 3 C) 3 D) 3 3

Use the unit circle to find the value of the trigonometric function.

20) sin 6

A) 3 3

B) 12 C) 3

2 D) 2

2

SHORT ANSWER. You must show all your work to receive full credit.

Complete the identity.

21) sin xcos x +

cos x sin x

= ?

Find the exact value of the indicated trigonometric function of .

22) cos = 47 , tan < 0 Find sin .

Solve the problem.

23) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 80 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 35°. What is the distance between the piling and the pier to the nearest foot?

24) A building 220 feet tall casts a 60 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.)

Use reference angles to find the exact value of the expression. Do not use a calculator.

25) tan -56

4