Cos 252 Degrees

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

What is cos 252°?

Answer

cos 252° =
−(√5 − 1)/4 ≈ −0.3090

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

≈ — rounded to 4 decimal places.

cos 252° = cos(180° + 72°) = −cos 72° = −(√5 − 1)/4

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

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

cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

xyOP

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

Highlighted: the projection on the x-axis — cosine, x ≈ −0.3090.

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: cos 72° = (√5 − 1)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
227°≈ −0.6820
234°−√(10 − 2√5)/4
240°−1/2
252°−(√5 − 1)/4
255°−(√6 − √2)/4
270°0
285°(√6 − √2)/4

FAQ

What is cos 252°?

cos 252° = −(√5 − 1)/4 ≈ −0.3090

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 0.7822 for cos 252?

The calculator is in radian mode (RAD): it takes cos 252 as the cosine of 252 radians, cos 252 rad ≈ 0.7822. Switch it to degrees (DEG): cos 252° = −(√5 − 1)/4 ≈ −0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also