Sin 78 Degrees

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

What is sin 78°?

Answer

sin 78° ≈
0.9781

Angle in radians: 78° = 13π/30. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places. An exact form of sin 78° in square roots exists, but it is unwieldy — nested radicals.

P(cos 78°, sin 78°) ≈ (0.2079, 0.9781)

xyOP

P(cos 78°, sin 78°) ≈ (0.2079, 0.9781)

Highlighted: the projection on the y-axis — sine, y ≈ 0.9781.

All four functions of 78°
FunctionExact valueDecimal
sin 78°—≈ 0.9781
cos 78°—≈ 0.2079
tan 78°—≈ 4.7046
cot 78°—≈ 0.2126

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
75°(√6 + √2)/4
76°≈ 0.9703
77°≈ 0.9744
78°≈ 0.9781
79°≈ 0.9816
80°≈ 0.9848
81°≈ 0.9877

FAQ

What is sin 78°?

sin 78° ≈ 0.9781

Is there an exact value of sin 78°?

Yes: 78° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: sin 78° ≈ 0.9781.

Why does a calculator show 0.5140 for sin 78?

The calculator is in radian mode (RAD): it takes sin 78 as the sine of 78 radians, sin 78 rad ≈ 0.5140. Switch it to degrees (DEG): sin 78° ≈ 0.9781. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also