Cos 75 Degrees

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

What is cos 75°?

Answer

cos 75° =
(√6 − √2)/4 ≈ 0.2588

Angle in radians: 75° = 5π/12. The point of the angle is in quadrant I, where cosine is positive.

≈ — rounded to 4 decimal places.

P(cos 75°, sin 75°) = ((√6 − √2)/4, (√6 + √2)/4)

cos 75° = cos(45° + 30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4

xyOP

P(cos 75°, sin 75°) ≈ (0.2588, 0.9659)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.2588.

All four functions of 75°
FunctionExact valueDecimal
sin 75°(√6 + √2)/4≈ 0.9659
cos 75°(√6 − √2)/4≈ 0.2588
tan 75°2 + √3≈ 3.7321
cot 75°2 − √3≈ 0.2679

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
72°(√5 − 1)/4
73°≈ 0.2924
74°≈ 0.2756
75°(√6 − √2)/4
76°≈ 0.2419
77°≈ 0.2250
78°≈ 0.2079

FAQ

What is cos 75°?

cos 75° = (√6 − √2)/4 ≈ 0.2588

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show 0.9218 for cos 75?

The calculator is in radian mode (RAD): it takes cos 75 as the cosine of 75 radians, cos 75 rad ≈ 0.9218. Switch it to degrees (DEG): cos 75° = (√6 − √2)/4 ≈ 0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also