Sin 690 Degrees

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

What is sin 690°?

Answer

sin 690° =
−1/2 = −0.5

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

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

sin 330° = sin(360° − 30°) = −sin 30° = −1/2

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.

sin 30° = 1/2

xyOP

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

Highlighted: the projection on the y-axis — sine, y = −0.5.

+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: sin 30° = 1/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
390°1/2
400°≈ 0.6428
450°1
540°0
570°−1/2
690°−1/2
720°0

FAQ

What is sin 690°?

sin 690° = −1/2 = −0.5

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: sin 690° = −1/2 = −0.5.

Why does a calculator show −0.9129 for sin 690?

The calculator is in radian mode (RAD): it takes sin 690 as the sine of 690 radians, sin 690 rad ≈ −0.9129. Switch it to degrees (DEG): sin 690° = −1/2 = −0.5. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also