Please complete 7 questions regarding trigonometry. YOU MUST SHOW STEPS OF WORK. Pls hand write on the pdf and send a picture of it back. I must send a scan of it back to turn it in.

MATH-UA 009: Algebra and Calculus

Written Worksheet 11

Due: Tuesday, December 10th, 11:55pm via GradeScope

Last written HW, mainly covers trigonometry; total 70 points

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your average for the final grade. This means you can take a “free spin” for any reason you want.

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or reduced points for insufficient work or sloppy work.

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Section

Instructor

Lecture Time & Location

002

Song Tian

T, 8:00-9:15AM, 194M 307

003

Song Tian

Th, 8:00-9:15AM, 194M 307

004

Shenxiong Li

T, 8:00-9:15AM, GODD B02

005

Xiaotong Ding

Th, 8:00-9:15AM, GCASL 269

007

Yunxiao Xiang

T, 9:30-10:45AM, MEYR 261

008

Yunxiao Xiang

Th, 9:30-10:45AM, 7E12 129

009

Shenxiong Li

T, 9:30-10:45AM, SILV 620

010

Xiaotong Ding

Th, 9:30-10:45AM, 7E12 123

Math-UA.009. Written Worksheet

Free Response

Please show all work and justification.

8 15

1. (12 points total) Verify that the point

,

is a point on the unit circle (3 points).

17 17

Compute following trigonometric angles (1.5 points each part):

A) sin θ =

B) cos θ =

C) tan θ =

D) csc θ =

E) sec θ =

F) cot θ =

2. (3 points) Suppose that θ =

π

. Find the area of the triangle.

3

2

Math-UA.009. Written Worksheet

3. (9 points total, 1.5 points each part) Consider the following right angle triangle

?

9

θ

12

Compute following trigonometric angles:

A) sin θ =

B) cos θ =

C) tan θ =

D) csc θ =

E) sec θ =

F) cot θ =

3

Math-UA.009. Written Worksheet

4. (12 points) Show your steps to answer the following questions:

(a) (4.5 points) Convert following angles in radians.

72◦ , 120◦ , 300◦

(b) (4.5 points) Convert following angles in degree.

5π 3π 7π

,

,

9 2 6

(c) (3 points) Compute the reference angle for each of the following angle.

5π 3π

,

, 200◦

3 2

4

Math-UA.009. Written Worksheet

5. (12 points, 1.5 each part) For each of the following angle:

(1) Compute the reference angle.

(2) Compute the output for sin, cos and tan function at given angle.

(a) 240◦

(b)

7π

4

5

Math-UA.009. Written Worksheet

6. (8 points) Simplify each of the following trigonometric expressions:

(a)

sin (30◦ ) + cos (0◦ ) − 2 tan (45◦ )

(b)

sin

π 2

4

π 2

− 2 + cos

4

(c)

sin (60◦ ) cos (30◦ ) − (tan (30◦ ))2

(d)

(tan (60◦ ))2 − (sec (60◦ ))2 + 1

6

Math-UA.009. Written Worksheet

7. (14 points) For each of the following trigonometric functions, write down the amplitude, period, and horizontal or vertical shift, if any; and then sketch at least one period

of the graph

(a) f (θ) = 3 cos θ − 7

(b) f (θ) = 2 sin (2θ − π)

7