The Graphs of Sine, Cosine and Tangent Functions
6.2
The Graphs of Sine, Cosine and Tangent Functions
The characteristics of sine graph, y = sin x:
has a maximum value of 1 when x = 90∘ and a minimum value of –1 when x = 270∘
intercepts x-axis at x = 0∘ , 180∘ , 360∘ (x-intercept)
intercepts -axis at y = 0 ( y -intercept)
The characteristics of cosine graph, y = cos x:
has a maximum value of 1 when x = 0∘ and x = 360∘ and a minimum value of –1 when x = 180∘
intercepts x-axis at (x-intercept)
intercepts y -axis at y = 1 (y -intercept)
The characteristics of tangent graph, y = tan x:
maximum value is ∞ and minimum value is −∞
intercepts x-axis at x = 0∘ , 180∘ , 360∘ (x-intercept)
intercepts y -axis at y = 0 ( y -intercept)
the values of tan 90∘ and tan 270∘ are undefined
The effects of changes in constants a, b and c on the graphs of trigonometric functions y = a sin bx + c, y = a cos bx + c and y = a tan bx + c
© 2024 Pandai.org All Rights Reserved
Example 5
The diagram below shows a graph of the function y = sin x for 0∘ ≤ x ≤ 360∘ . Sketch each of the following trigonometric functions on the
same axes.
(a) y = 2 sin x
(c) y = sin x + 1
(b) y = sin 2x
(d) y = 2 sin 2x
Solution:
© 2024 Pandai.org All Rights Reserved
© 2024 Pandai.org All Rights Reserved
© 2024 Pandai.org All Rights Reserved