Cos 690 Degrees

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

What is cos 690°?

Answer

cos 690° =
√3/2 ≈ 0.8660

Angle in radians: 690° = 23π/6. 690° = 360° + 330° — a full turn plus 330°, quadrant IV, where cosine is positive.

≈ — rounded to 4 decimal places.

cos 690° = cos(690° − 360°) = cos 330°

cos 330° = cos(360° − 30°) = cos 30° = √3/2

P(cos 690°, sin 690°) = (√3/2, −1/2)

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

cos 30° = √(1 − 1/4) = √3/2

xyOP

P(cos 690°, sin 690°) ≈ (0.8660, −0.5)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.8660.

+1 turn: the drawing shows 330°.

All four functions of 690°
FunctionExact valueDecimal
sin 690°−1/2−0.5
cos 690°√3/2≈ 0.8660
tan 690°−√3/3≈ −0.5774
cot 690°−√3≈ −1.7321

Reference angle: cos 30° = √3/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
390°√3/2
400°≈ 0.7660
450°0
540°−1
570°−√3/2
690°√3/2
720°1

FAQ

What is cos 690°?

cos 690° = √3/2 ≈ 0.8660

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cos 690° = √3/2 ≈ 0.8660.

Why does a calculator show 0.4081 for cos 690?

The calculator is in radian mode (RAD): it takes cos 690 as the cosine of 690 radians, cos 690 rad ≈ 0.4081. Switch it to degrees (DEG): cos 690° = √3/2 ≈ 0.8660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also