Tan 135 Degrees

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

What is tan 135°?

Answer

tan 135° =
−1

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

tan 135° = tan(180° − 45°) = −tan 45° = −1

tan 135° = sin 135° / cos 135° = (√2/2) / (−√2/2) = −1

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

tan 45° = 1/1 = 1

xyOP

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

T(1, tan 135°) = (1, −1) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

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: tan 45° = 1

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
127°≈ −1.3270
130°≈ −1.1918
134°≈ −1.0355
135°−1
140°≈ −0.8391
142°≈ −0.7813
144°−√(5 − 2√5)

FAQ

What is tan 135°?

tan 135° = −1

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: tan 135° = −1.

Why does a calculator show −0.0887 for tan 135?

The calculator is in radian mode (RAD): it takes tan 135 as the tangent of 135 radians, tan 135 rad ≈ −0.0887. Switch it to degrees (DEG): tan 135° = −1. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also