6.3 graph of sine, cosine and tangent functions Homeroom Sir Hafiz

ADDITIONAL MATHEMATICS

Graph of
Trigonometric

Functions

Homeroom Sir Hafiz - MRSM Baling

CHAPTER 6.3 KSSM
CHAPTER 10 IGCSE

Graph of Sine and Cosine Function

Properties of graphs of y = sin x and y = cos x

sinusoidal
max value = 1, min value = –1
amplitude of 1 unit
period = 360° or 2π rad

y = sin x max value

y = cos x min value

Graph of Tangent Function

Properties of graphs of y = tan x

not sinusoidal
no max & min value but has asymptotes
amplitude of 1 unit
period = 180° or π rad

y = tan x asymptotes







Sine Graph

General equation

y = a sin bx + c Position

Amplitude / Max@Min

How many cycles in 360/2π

y = sin x

y = sin 2x

y = 2 sin x

Cosine Graph

General equation

y = a cos bx + c Position

Amplitude / Max@Min

How many cycles in 360/2π

y = cos x

y = cos 2x

y = 3 - cos x

Tangent Graph

General equation

y = a tan bx + c Position

Amplitude / Max@Min

How many cycles in 360/2π

y = tan x

y = tan 2x

y = −tan x
y = tan x + 2

Topic Questions

MOE format

1. Sketch the graph of each of the following trigonometric functions for

0 ≤ x ≤ 2π.

(a) y = 3 sin x (d) y = −3 cos 2x + 1

(b) y = 3 cos 2x (e) y = |3 sin 2x|

(c) y = sin x − 2 (f) y = −tan x

2. Sketch the graph of y = 4 cos 2x for 0 ≤ x ≤ 2π.

On the same axes, sketch the straight line and hence,

state the number of solutions to the equation 4π cos 2x = x.

3. Sketch on the same axes the curves of y = 4 cos 2x and y = 2|sin x|
for 0 ≤ x ≤ 2π. Hence, state the number of solutions to the
equation 4 cos 2x − 2|sin x| = 0

IGCSE format
0606/13/O/N/12

0606/23/M/J/16