5 homework of Math 1001

MATH 1001: Pre-Calculus Mathematics 1

TRU Open Learning

Assignment 6: 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 ) =

tan 𝑥−√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]

Select questions associated with the following course textbook are used with

permission from Cengage Learning:

Swokowski, E. W., & Cole, J. A. (2012). Precalculus: Functions and graphs

(12th ed.). Belmont, CA: Brooks/Cole, Cengage Learning