Sin 252 Degrees

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

What is sin 252°?

Answer

sin 252° =
−√(10 + 2√5)/4 ≈ −0.9511

Angle in radians: 252° = 7π/5. The point of the angle is in quadrant III, where sine is negative.

≈ — rounded to 4 decimal places.

sin 252° = sin(180° + 72°) = −sin 72° = −√(10 + 2√5)/4

P(cos 252°, sin 252°) = (−(√5 − 1)/4, −√(10 + 2√5)/4)

Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

sin 72° = cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

xyOP

P(cos 252°, sin 252°) ≈ (−0.3090, −0.9511)

Highlighted: the projection on the y-axis — sine, y ≈ −0.9511.

All four functions of 252°
FunctionExact valueDecimal
sin 252°−√(10 + 2√5)/4≈ −0.9511
cos 252°−(√5 − 1)/4≈ −0.3090
tan 252°√(5 + 2√5)≈ 3.0777
cot 252°√(25 − 10√5)/5≈ 0.3249

Reference angle: sin 72° = √(10 + 2√5)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
227°≈ −0.7314
234°−(√5 + 1)/4
240°−√3/2
252°−√(10 + 2√5)/4
255°−(√6 + √2)/4
270°−1
285°−(√6 + √2)/4

FAQ

What is sin 252°?

sin 252° = −√(10 + 2√5)/4 ≈ −0.9511

How are sin 18° and cos 72° related?

They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

Why does a calculator show 0.6230 for sin 252?

The calculator is in radian mode (RAD): it takes sin 252 as the sine of 252 radians, sin 252 rad ≈ 0.6230. Switch it to degrees (DEG): sin 252° = −√(10 + 2√5)/4 ≈ −0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also