Hr. Cg. Khadijah

6.3 Graph Of Sine,
Cosine and

Tangent Function

• The graphs for the trigonometric functions y = a sin bx + c, y = a cos bx + c and y = a
tan bx + c, where a, b, c are constant and b > 0, can be constructed using any
dynamic geometric software or just manually using tables of value and graph papers

The graphs of y = sin x and y = cos x The graph y = tan x properties:

properties : • Not sinusoidal
• Sinusoidal • No max or min value
• Max value = 1 • Repeats itself every 180° or π rad interval
• Min value = -1 • Period = 180° or π rad
• Amplitude = 1 unit • Not defined at x = 90° and x = 270°
• Repeats itself every 360° or 2π • Curve approaches the line x = 90° and x = 270°
• Period = 360° or 2π
but not touch the line
• This line called asymptote

The value of a, b, and c in the function y = a sin bx + c affect
the amplitude, the period and the position of the graph

Similar transformations can be done on the graphs y = cos x and y = tan x. it is found
that the original shapes of the graphs remain unchanged. The effects of changing
the value of a, b, and c on the graph can be summarised in the following table:

Sine Graph

y = sin x y = sin 2x
Change in b
Number of cycle change

Sine Graph

y = 2 sin x y = sin x + 2
Change in a Change in c
Number of max and min Graph location change
value change

Sine Graph

y = -sin x y = |sin x|
Change in sin Addition absolute value
The graph reverse
bracket
The graph upward

Cosine Graph

y = cos x y = cos 2x
Change in b
Number of cycle change

Cosine Graph

y = 2 cos x y = cos x + 2
Change in a Change in c
Number of max and min Graph location change
value change

Cosine Graph

y = -cos x y = |cos x|
Change in sin Addition absolute value
The graph reverse
bracket
The graph upward

Tangent Graph

y = tan x y = tan 2x
Change in b
Number of cycle change

Tangent Graph

y = 2 tan x y = tan x + 2
Change in a Change in c
Number of max and min Graph location change
value change

Tangent Graph

y = -tan x y = |tan x|
Change in sin Addition absolute value
The graph reverse
bracket
The graph upward