Tan 315 Degrees

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

What is tan 315°?

Answer

tan 315° =
−1

Angle in radians: 315° = 7π/4. The point of the angle is in quadrant IV, where tangent is negative.

tan 315° = tan(360° − 45°) = −tan 45° = −1

tan 315° = sin 315° / cos 315° = (−√2/2) / (√2/2) = −1

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

tan 45° = 1/1 = 1

xyOP

P(cos 315°, sin 315°) ≈ (0.7071, −0.7071)

T(1, tan 315°) = (1, −1) — where line OP meets the line x = 1.

All four functions of 315°
FunctionExact valueDecimal
sin 315°−√2/2≈ −0.7071
cos 315°√2/2≈ 0.7071
tan 315°−1−1
cot 315°−1−1

Reference angle: tan 45° = 1

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
288°−√(5 + 2√5)
300°−√3
306°−√(25 + 10√5)/5
315°−1
324°−√(5 − 2√5)
330°−√3/3
341°≈ −0.3443

FAQ

What is tan 315°?

tan 315° = −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 315° = −1.

Why does a calculator show 1.1173 for tan 315?

The calculator is in radian mode (RAD): it takes tan 315 as the tangent of 315 radians, tan 315 rad ≈ 1.1173. Switch it to degrees (DEG): tan 315° = −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