Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.3

values are in fact equal:

sin293◦ =− 0 , 92...

−sin67◦ =− 0 , 92...

Example 4: More Complicated

QUESTION

Evaluate without using acalculator:

tan^2210 ◦− (1 + cos120◦)sin^2225 ◦

SOLUTION

tan^2210 ◦− (1 + cos120◦)sin^2225 ◦

= [tan(180◦+ 30◦)]^2 − [1 + cos(180◦− 60 ◦)] .[sin(180◦+ 45◦)]^2

= (tan30◦)^2 − [1 + (−cos60◦)] .(−sin45◦)^2

=

�

1

√

3

� 2

−

�

1 −

1

2

�

.

�

−

1

√

2

� 2

=

1

3

−

�

1

2

��

1

2

�

=

1

3

−

1

4

=

1

12

Exercise 17 - 9

1. Write these equations as a function of θ only:

(a) sin(180◦− θ)

(b) cos(180◦− θ)

(c) cos(360◦− θ)

(d) cos(360◦+ θ)

(e) tan(180◦− θ)

(f) cos(360◦+ θ)

2. Write the following trig functions as a function of an acute angle: