Pre-Calculus homework

MATH 115 QUIZ 4 November, 2019 Instructor: I. Izmirli

NAME: _______________________________

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

INSTRUCTIONS

 The quiz is worth 100 points. There are 10 problems.

 Each problem is worth 10 points

 This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission).

You may take as much time as you wish, provided you turn in your quiz no later than this Sunday.

 Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable

also. In your document, be sure to include your name and the assertion of independence of work.

 General quiz tips and instructions for submitting work are posted in the Quizzes module.

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

Your answers may involve square roots. Rationalize denominators where appropriate.

1.

(a) State the reference angle associated with 150.

(b) State the exact value of sin(150).

(c) State the exact value of tan(2π/3).

2. Given a right triangle having an acute angle  of 24and hypotenuse of length 40.0, find the measurement of the other angle and the other sides.

3. Suppose that the point (√11, −5) lies on the terminal side of an angle  in standard position. Find

the exact values of the six trigonometric functions of .

sin( ) =

cos( ) =

tan( ) =

csc( ) =

sec( ) =

cot( ) =

4. A person is sitting on the ground between the Acme and Baker buildings. The person is 34 feet from

the Acme building. The Baker building is 58.2 feet tall. From the person’s point of view, the angle of

elevation to the top of the Acme building is 63 and the angle of elevation to the top of Baker building

is 45.

(a) How tall is the Acme building?

(b) How far apart are the two buildings?

Report the values to the nearest tenth of a foot.

5. Use a sum or a difference identity to find the exact value of cos(75).

Acme

Baker

63 45

58.2’

34’

6. Given that sin( ) = 4/7 for an angle  in Quadrant II, find the exact values of each of the following:

(a) cos( )

(b) sin(2 )

(c) cos(2 )

7. Consider 𝑦 = 4 𝑠𝑖𝑛 (6𝑡 − 3𝜋

2 )

(a) State the amplitude.

(b) State the period.

(c) State the phase shift.

8. State all of the exact solutions of the equation sin(2x) = 1/2 in the interval [0, 2).

9. Prove the identity         sintancossec  .

HINT: Rewrite each side of the expression using sines and cosines, simplify and apply a Pythagorean identity.

10.

(a) Find the exact value of arcsec(2).

(b) Find the exact value of tan (arcsin ( √3

2 )).

(c) Find the exact value of arcsin (sin 3𝜋

2 ).

(d) Find the exact value of arccos (tan 5𝜋

4 ).