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# 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

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

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

y = cos x
Cosine Value

### Period, Amplitude: y = cos x

y = cos x

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

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)

y = a tan bx

Period: |b|

y = 4 tan 2x
Period?
Solution