# Sine: Value

How to find the value of sine (trigonometry): 1 example and its solution. + Sine values of commonly used angles.

## Example

First, find the reference angle of 3π/4.

3π/4 is between π/2 and π.

So draw the terminal side on quadrant II.

Then the reference angle is

π - 3π/4.

π = 4π/4

4π/4 - 3π/4 = π/4

So the reference angle is π/4.

Draw a right triangle like this.

The central angle is π/4: 45º.

So this is a 45-45-90 triangle.

So the base is -1.

The height is 1.

And the hypotenuse is √2.

sin 3π/4 is the sine of the right triangle.

Sine is SOH:

Sine,

Opposite side (1),

Hypotenuse (√2).

So sin 3π/4 = 1/√2.

Rationalize the denominator √2

by multiplying √2/√2.

Then √2/2.

So sin 3π/4 = √2/2.

## Sine Values of Commonly Used Angles

These are the sine values

of commonly used angles.

θ = 0

The adjacent side (base) is 1.

The opposite side (height) is 0.

The hypotenuse is 1.

SOH:

Sine,

Opposite side (0),

Hypotenuse (1).

So sin 0 = 0/1 = 0.

θ = π/6

This is a 30-60-90 triangle.

The adjacent side (base) is √3.

The opposite side (height) is 1.

The hypotenuse is 2.

SOH:

Sine,

Opposite side (1),

Hypotenuse (2).

So sin π/6 = 1/2.

θ = π/4

This is a 45-45-90 triangle.

The adjacent side (base) is 1.

The opposite side (height) is 1.

The hypotenuse is √2.

SOH:

Sine,

Opposite side (1),

Hypotenuse (√2).

So sin π/4 = 1/√2 (= √2/2).

θ = π/3

This is a 30-60-90 triangle.

The adjacent side (base) is 1.

The opposite side (height) is √3.

The hypotenuse is 2.

SOH:

Sine,

Opposite side (√3),

Hypotenuse (2).

So sin π/3 = √3/2.

θ = π/2

The adjacent side (base) is 0.

The opposite side (height) is 1.

The hypotenuse is 1.

SOH:

Sine,

Opposite side (1),

Hypotenuse (1).

So sin π/2 = 1/1 = 1.