Cos 78 Degrees

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

What is cos 78°?

Answer

cos 78° ≈
0.2079

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

≈ — rounded to 4 decimal places. An exact form of cos 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 x-axis — cosine, x ≈ 0.2079.

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 ↑

Cosine of nearby angles

Anglecos
75°(√6 − √2)/4
76°≈ 0.2419
77°≈ 0.2250
78°≈ 0.2079
79°≈ 0.1908
80°≈ 0.1736
81°≈ 0.1564

FAQ

What is cos 78°?

cos 78° ≈ 0.2079

Is there an exact value of cos 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: cos 78° ≈ 0.2079.

Why does a calculator show −0.8578 for cos 78?

The calculator is in radian mode (RAD): it takes cos 78 as the cosine of 78 radians, cos 78 rad ≈ −0.8578. Switch it to degrees (DEG): cos 78° ≈ 0.2079. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also