Sin 75 Degrees

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

What is sin 75°?

Answer

sin 75° =
(√6 + √2)/4 ≈ 0.9659

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

≈ — rounded to 4 decimal places.

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

sin 75° = sin(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 y-axis — sine, y ≈ 0.9659.

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 ↑

Sine of nearby angles

Anglesin
72°√(10 + 2√5)/4
73°≈ 0.9563
74°≈ 0.9613
75°(√6 + √2)/4
76°≈ 0.9703
77°≈ 0.9744
78°≈ 0.9781

FAQ

What is sin 75°?

sin 75° = (√6 + √2)/4 ≈ 0.9659

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 −0.3878 for sin 75?

The calculator is in radian mode (RAD): it takes sin 75 as the sine of 75 radians, sin 75 rad ≈ −0.3878. Switch it to degrees (DEG): sin 75° = (√6 + √2)/4 ≈ 0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also