MATH-UA 009 New York University Trigonometry Questions

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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Mark an “X” next to your lab/recitation section
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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