Analytic Trigonometric Functions

Analytic Trigonometric Functions
(52 marks, 7%)
Complete the following questions from the textbook. Show all your work, as full credit
will not be given for inadequately explained answers. This assignment is worth 7% of
your final grade and will be marked out of 52. For detailed instructions on how to
submit your assignments go to “How to Send Assignments for Grading” in your
Course Guide.
Section 6.1
1) Page 421, Q. 20 [4 marks]
Section 6.2
2) Page 432, Q. 34 [4 marks]
3) Find the solutions of the equation 4 cos2 𝑥 − 4 = −1 that are in the interval
[0,2𝜋). [4 marks]
4) Page 433, Q. 50 [5 marks]
Section 6.3
5) Find the exact values of tan (
5𝜋
12) and sin (
11𝜋
12 ). The final answer should not
have radicals in the denominator. [5 marks]
6) Page 444, Q. 20 [6 marks]
7) Verify the identity tan (𝑥 −
𝜋
3
) =
tan𝑥−√3
√3 tan 𝑥+1
. [4 marks]
Section 6.4
8) Find the exact values of sin(2𝜃), cos(2𝜃), and tan(2𝜃) when sin 𝜃 = −
7
12
and
180∘ < 𝜃 < 270∘
. [6 marks]
Section 6.6
9) Find the exact values of the following expressions:
a) cos−1
(
√3
2
) [2 marks]
b) tan (tan−1
(−
√3
10)) [2 marks]
2 Assignment 6
TRU Open Learning
10) Page 472, Q. 54 [ 5 marks]
11) Page 473, Q. 74 [5 marks