Cos 135 Degrees

Sin, Cos, Tan, Cot of an Angle
Function
Angle (°)

What is cos 135°?

Answer

cos 135° =
−√2/2 ≈ −0.7071

Angle in radians: 135° = 3π/4. The point of the angle is in quadrant II, where cosine is negative.

≈ — rounded to 4 decimal places.

cos 135° = cos(180° − 45°) = −cos 45° = −√2/2

P(cos 135°, sin 135°) = (−√2/2, √2/2)

An isosceles right triangle with legs 1: the hypotenuse is √2.

cos 45° = 1/√2 = √2/2

xyOP

P(cos 135°, sin 135°) ≈ (−0.7071, 0.7071)

Highlighted: the projection on the x-axis — cosine, x ≈ −0.7071.

All four functions of 135°
FunctionExact valueDecimal
sin 135°√2/2≈ 0.7071
cos 135°−√2/2≈ −0.7071
tan 135°−1−1
cot 135°−1−1

Reference angle: cos 45° = √2/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
127°≈ −0.6018
130°≈ −0.6428
134°≈ −0.6947
135°−√2/2
140°≈ −0.7660
142°≈ −0.7880
144°−(√5 + 1)/4

FAQ

What is cos 135°?

cos 135° = −√2/2 ≈ −0.7071

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cos 135° = −√2/2 ≈ −0.7071.

Why does a calculator show −0.9961 for cos 135?

The calculator is in radian mode (RAD): it takes cos 135 as the cosine of 135 radians, cos 135 rad ≈ −0.9961. Switch it to degrees (DEG): cos 135° = −√2/2 ≈ −0.7071. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also