Cot 315 Degrees

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

What is cot 315°?

Answer

cot 315° =
−1

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

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

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

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

cot 45° = 1/1 = 1

xyOP

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

C(cot 315°, 1) = (−1, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

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: cot 45° = 1

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
288°−√(25 − 10√5)/5
300°−√3/3
306°−√(5 − 2√5)
315°−1
324°−√(25 + 10√5)/5
330°−√3
341°≈ −2.9042

FAQ

What is cot 315°?

cot 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: cot 315° = −1.

Why does a calculator show 0.8950 for cot 315?

The calculator is in radian mode (RAD): it takes cot 315 as the cotangent of 315 radians, cot 315 rad ≈ 0.8950. Switch it to degrees (DEG): cot 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