Cos 570 Degrees

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

What is cos 570°?

Answer

cos 570° =
−√3/2 ≈ −0.8660

Angle in radians: 570° = 19π/6. 570° = 360° + 210° — a full turn plus 210°, quadrant III, where cosine is negative.

≈ — rounded to 4 decimal places.

cos 570° = cos(570° − 360°) = cos 210°

cos 210° = cos(180° + 30°) = −cos 30° = −√3/2

P(cos 570°, sin 570°) = (−√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 570°, sin 570°) ≈ (−0.8660, −0.5)

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

+1 turn: the drawing shows 210°.

All four functions of 570°
FunctionExact valueDecimal
sin 570°−1/2−0.5
cos 570°−√3/2≈ −0.8660
tan 570°√3/3≈ 0.5774
cot 570°√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 570°?

cos 570° = −√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 570° = −√3/2 ≈ −0.8660.

Why does a calculator show −0.1978 for cos 570?

The calculator is in radian mode (RAD): it takes cos 570 as the cosine of 570 radians, cos 570 rad ≈ −0.1978. Switch it to degrees (DEG): cos 570° = −√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