Sin 315 Degrees

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

What is sin 315°?

Answer

sin 315° =
−√2/2 ≈ −0.7071

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

≈ — rounded to 4 decimal places.

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

P(cos 315°, sin 315°) = (√2/2, −√2/2)

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

sin 45° = 1/√2 = √2/2

xyOP

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

Highlighted: the projection on the y-axis — sine, y ≈ −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: sin 45° = √2/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
288°−√(10 + 2√5)/4
300°−√3/2
306°−(√5 + 1)/4
315°−√2/2
324°−√(10 − 2√5)/4
330°−1/2
341°≈ −0.3256

FAQ

What is sin 315°?

sin 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: sin 315° = −√2/2 ≈ −0.7071.

Why does a calculator show 0.7451 for sin 315?

The calculator is in radian mode (RAD): it takes sin 315 as the sine of 315 radians, sin 315 rad ≈ 0.7451. Switch it to degrees (DEG): sin 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