algebra 101

simple algebra questions , make it pdf

Math-UA.009. Written Homework
MATH-UA-009 — Algebra, Trigonometry and Functions
Professor Ross Flek
Name:
NetID:
Homework Assignment #11
Due Date: December 15th, 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.
• There are three main ways you might want to write up your work.
– Write on this pdf using a tablet
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them into a single pdf file. Gradescope will only allow pdf files to be
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
significant portion of your score.
• When appropriate put a box or circle around your final answer.
• 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. (7 points) Find the exact value of each of the following
 
1
−1
(a) sin
−
2
(b) cos−1 (−1)
(c) tan−1 (−1)
(d) sin−1 (1)
(e) cos−1
√ !
2
−
2
(f) cos−1 (−0.5)
(g) tan−1 (1)
2
Math-UA.009. Written Homework
2. (8 points) Find the exact value of each of the following
  
5π
−1
(a) sin
sin
4
(b) sin
−1
−1
(c) cos


sin
2π
3

  
7π
cos
6
(d) cos cos−1
√ !!
3
−
2
3
Math-UA.009. Written Homework
3. (6 points) Find the exact value of the expressions below. Show all work.

 
1
−1
(a) (3 points) cos tan
3

−1
(b) (3 points) tan sin
 
2
3
4
Math-UA.009. Written Homework
4. (9 points) Solve the following equations. In each case, give a general formula
for all solutions.
√
(a) (3 points) 2 cos (θ) − 1 = 0
(b) (3 points) 2 sin (θ) + 1 = 0
(c) (3 points) 4 sin2 (θ) − 3 = 0
5