University of the Southern Caribbean
School of Sciences and Technology
Dept. of computer Science, Mathematics and Technology
Pre-calculus Trigonometry
Final assessment
December 8, 2021
Total marks 50
Instructions: Answer ALL the questions.
Read the questions carefully before you answer.
Question FOUR carries 22 marks.
Do not type the answers. Answer the questions on sheets of paper. It should be neat and
clearly visible for marking.
1
Prove that each of the following equations are true.
a. cos⁡(90 − A) ⁡ = ⁡𝑠𝑖𝑛𝐴⁡⁡⁡⁡
b. 𝑠𝑖𝑛2 𝑥⁡(𝑐𝑜𝑡 2 𝑥 + 1) = 1
c. sin(−∅) sec(−∅) cot(−∅) = 1
[ 8 marks]
2
Convert the following without using calculator.
a. 225⁡°⁡⁡𝑎𝑛𝑑⁡150⁡° to radians
[4 marks]
5𝜋⁡⁡
11𝜋
⁡⁡𝑎𝑛𝑑⁡⁡ 6
3⁡
b. ⁡
to degrees
3. This question is based on circular functions. Use Figure below to answer this question.
.
a)
Given θ =
i)
ii)
5𝜋
4
Express x and y coordinate of P at the given angle in terms of trigonometric
functions.
[2 marks]
Find 𝑐𝑜𝑠𝑒𝑐⁡𝜃, sec 𝜃 tan θ ⁡𝑎𝑛𝑑 cot 𝜃 trigonometric functions
[4 marks]
b) Find all values of θ between 0 and 2π for which cot θ = √3
4
[ 2 marks]
a) Define amplitude and period. [2 marks]
𝜋
𝜋
3𝜋
2
2
2
b)Graph 𝑦 = sin 𝑥 and 𝑦 = sin (𝑥 + ⁡ ) ⁡𝑖𝑓 − ⁡ ⁡ ≤ 𝑥 ≤ ⁡
on the same graph
sheet/paper.
i) Choose appropriate scales for x and y axis.
[2 marks]
ii) Calculate the y coordinates for the given x coordinates and tabulate them for both
the trigonometric functions.
[8 marks]
iii) Plot the points for the first equation and join them with a free hand. Likewise do the
same for the second equation as well
[ 4 marks]
iv) On the graph show the amplitude and period of both trigonometric equations.
[2 marks]
v) What conclusions you draw by looking at both the graphs.
[ 4 marks]
5.
a. Find the missing parts of triangle ABC if B = 340, C = 82°, and a = 5.6 cm.
[6 marks]
(Hint: Use The law of Sines)
b. Find its area by using one of the formulae learned in class
[2 marks]
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