Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.3

(a) In the figure P and P�lie on the cir-

cle with radius 2. OP makes an angle

θ = 30◦with the x-axis. P thus has co-

ordinates (

√

3;1). P�is the reflection of

P about the line y = x. Using symmetry,

write down the coordinates of P�.

(b) Using the coordinates for P�determine

sin(90◦−θ), cos(90◦−θ) and tan(90◦−

θ).

(c) From your results tryand determine a re-

lationship between the function values of

(90◦− θ) and θ.

�P

0 x

y

θ

�

θ

P�

2

2

90 ◦− θ

2. Function values of (90◦+ θ)

(a) In the figure P and P�lie on the cir-

cle with radius 2. OP makes an angle

θ = 30◦with the x-axis. P thus has co-

ordinates (

√

3;1). P�is the rotation of

P through 90 ◦. Using symmetry, write

down the coordinates of P�. (Hint: con-

sider P�as the reflection of P about the

line y = x followed by a reflectionabout

the y-axis)

(b) Using the coordinates for P�determine

sin(90◦+θ), cos(90◦+θ) and tan(90◦+

θ).

(c) From your results tryand determine a re-

lationship between the function values of

(90◦+ θ) and θ.

θ

�P

0 x

y

θ

P�

�

90 ◦+ θ

2

2

Complementary anglesare positive acute angles that add up to 90 ◦. For example 20 ◦and 70 ◦are
complementary angles.

Sine and cosine are known as co-functions. Two functions are called co-functions if f(A) = g(B)
whenever A + B = 90◦(i.e. A and B are complementary angles). The other trig co-functions are
secant and cosecant, and tangent and cotangent.

The function value of anangle is equal to the co-function of its complement (the co-co rule).

Thus for sine and cosinewe have

sin(90◦− θ) = cos θ

cos(90◦− θ) = sin θ

Example 5: Co-function Rule

QUESTION

Write each of the following in terms of 40 ◦using sin(90◦−θ) = cos θ and cos(90◦−θ) = sin θ.

1. cos50◦


2. sin320◦


3. cos230◦