Cos 315 Degrees

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

What is cos 315°?

Answer

cos 315° =
√2/2 ≈ 0.7071

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

≈ — rounded to 4 decimal places.

cos 315° = cos(360° − 45°) = cos 45° = √2/2

P(cos 315°, sin 315°) = (√2/2, −√2/2)

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

cos 45° = 1/√2 = √2/2

xyOP

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

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

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: cos 45° = √2/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
288°(√5 − 1)/4
300°1/2
306°√(10 − 2√5)/4
315°√2/2
324°(√5 + 1)/4
330°√3/2
341°≈ 0.9455

FAQ

What is cos 315°?

cos 315° = √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 315° = √2/2 ≈ 0.7071.

Why does a calculator show 0.6669 for cos 315?

The calculator is in radian mode (RAD): it takes cos 315 as the cosine of 315 radians, cos 315 rad ≈ 0.6669. Switch it to degrees (DEG): cos 315° = √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