Ximpledu

Trigonometric Function Graph

See how to find the amplitude/period of a trigonometric function graph
(sine, cosine, tangent).
5 examples and their solutions.

Sine Graph

Graph

y = sin x
Sine Value

Period, Amplitude: y = sin x

y = sin x

Amplitude: 1
Period:
Period: 2π
→ If you move y = sin x
(x, y) → (x + 2π, y),
you get the same graph.
→ sin x = sin (x - 2π)
→ Periodic function
Translation: Function

Period, Amplitude: y = a sin bx

y = a sin bx


Amplitude: |a|
Period: |b|

Example

y = 3 sin 2x
Amplitude, period?
Solution

Example

y = a sin (bx + c) + d (0 ≤ x ≤ 2π)


a, b, c, d = ?
Solution

Cosine Graph

Graph

y = cos x
Cosine Value

Period, Amplitude: y = cos x

y = cos x

Amplitude: 1
Period:
Period: 2π
→ cos x = cos (x - 2π)

Period, Amplitude: y = a cos bx

y = a cos bx


Amplitude: |a|
Period: |b|

Example

y = 2 cos 3x
Amplitude, period?
Solution

Example

y = a cos (bx + c) + d (0 ≤ x ≤ 2π)


a, b, c, d = ?
Solution

Tangent Graph

Graph

y = tan x

Asymptotes: y = π/2, 3π/2, ...
Tangent Value

Period: y = tan x

y = tan x


Period: π
Period: π
→ tan x = tan (x - π)

Period: y = a tan bx

y = a tan bx


Period: |b|

Example

y = 4 tan 2x
Period?
Solution