simple algebra questions, make it pdf

Math-UA.009. Written Homework

MATH-UA-009 — Algebra, Trigonometry and Functions

Name:

NetID:

Homework Assignment #10

Due Date: December 11th, 2023, 11:59 PM

• This homework should be submitted via Gradescope by 23:59 on the date

listed above. You can find instructions on how to submit to Gradescope on

our Campuswire channel.

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uploaded.

• You must show all work. You may receive zero or reduced points for

insufficient work. Your work must be neatly organised and written.

You may receive zero or reduced points for incoherent work.

• If you are writing your answers on anything other than this sheet, you should

only have one question per page. You can have parts a), b) and c) on the

page for example, but problems 1) and 2) should be on separate pages.

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page that your answer appears on. If you do not you will be docked a

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• The problems on this assignment will be graded on correctness and completeness.

• These problems are designed to be done without a calculator. Whilst there is

nothing stopping you using a calculator when working through this assignment,

be aware of the fact that you are not permitted to use calculators on exams

so you might want to practice without one.

1

Math-UA.009. Written Homework

1. For each of the following angles, determine the following:

• The quadrant the angle lies in

• The reference angle

• The values of sin (θ), cos (θ) and tan (θ)

(a) (3 points) θ = −π/4

(b) (3 points) θ = π/6

(c) (3 points) θ = 5π/6

(d) (3 points) θ = −5π/6

(e) (3 points) θ = −2π/3

2

Math-UA.009. Written Homework

(f) (3 points) θ = −π

(g) (3 points) θ = 2π/3

(h) (3 points) θ = 7π/6

(i) (3 points) θ = 3π/2

(j) (3 points) θ = −3π/4

3

Math-UA.009. Written Homework

2. For each of the following triangles, find the value of

• sin (θ)

• cos (θ)

• tan (θ)

(a)

4

θ

8

(3 points)

(b)

3

θ

7

(3 points)

(c)

10

θ

6

(3 points)

4

Math-UA.009. Written Homework

(d)

12

θ

8

(3 points)

(e)

9

θ

15

(3 points)

(f)

9 θ

√

481

(3 points)

5

Math-UA.009. Written Homework

3. (a) (3 points) Find sin (θ) given that cos (θ) = 1/5 and θ is in quadrant IV.

(b) (3 points) Find tan (θ) given that sin (θ) = 1/3 and θ is in quadrant II.

6

Math-UA.009. Written Homework

4. (4 points) Find the amplitude, period and horizontal shift of the function, and

graph one complete period

π

y = −3 sin 2 x +

4

5. (4 points) Find the amplitude and period of the function, and sketch its graph.

y =1+

7

π

1

cos

x

2

2