Trigonometric value

Sin(135°) = √2/2

Sine — the y-coordinate of the corresponding unit-circle point, or opposite/hypotenuse in a right triangle.

How to derive sin(135°)

sin(135°)=22sin(135°) = \dfrac{\sqrt{2}}{2}

135° is in quadrant II. Reference angle = 180° − 135° = 45°, and sine is positive in quadrant II, so sin(135°) = +sin(45°) = √2/2.

Unit-circle context

The angle 135° corresponds to 3π/4 radians and sits Quadrant II on the unit circle.

Its reference angle is 45°, which is why sin(135°) shares its absolute value with sin(45°).

Other trig values at 135°

Related sin values

Frequently asked

What is the exact value of sin(135°)?
The exact value is √2/2. Its decimal approximation is 0.70711.
How do you derive sin(135°)?
135° is in quadrant II. Reference angle = 180° − 135° = 45°, and sine is positive in quadrant II, so sin(135°) = +sin(45°) = √2/2.
What is 135° in radians?
135° equals 3π/4 radians (multiply degrees by π/180).

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