Algebra 101

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
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our Campuswire channel.
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insufficient work. Your work must be neatly organised and written.
You may receive zero or reduced points for incoherent work.
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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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• 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

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