Trigonometric value

Cos(135°) = -√2/2

Cosine — the x-coordinate of the corresponding unit-circle point, or adjacent/hypotenuse in a right triangle.

How to derive cos(135°)

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

135° is in quadrant II. Reference angle = 45°, cosine negative in Q2, so cos(135°) = −cos(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 cos(135°) shares its absolute value with cos(45°).

Other trig values at 135°

Related cos values

Frequently asked

What is the exact value of cos(135°)?
The exact value is -√2/2. Its decimal approximation is -0.70711.
How do you derive cos(135°)?
135° is in quadrant II. Reference angle = 45°, cosine negative in Q2, so cos(135°) = −cos(45°) = −√2/2.
What is 135° in radians?
135° equals 3π/4 radians (multiply degrees by π/180).

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