Sin 195 Degrees

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

What is sin 195°?

Answer

sin 195° =
−(√6 − √2)/4 ≈ −0.2588

Angle in radians: 195° = 13π/12. The point of the angle is in quadrant III, where sine is negative.

≈ — rounded to 4 decimal places.

sin 195° = sin(180° + 15°) = −sin 15° = −(√6 − √2)/4

P(cos 195°, sin 195°) = (−(√6 + √2)/4, −(√6 − √2)/4)

sin 15° = sin(45° − 30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4

xyOP

P(cos 195°, sin 195°) ≈ (−0.9659, −0.2588)

Highlighted: the projection on the y-axis — sine, y ≈ −0.2588.

All four functions of 195°
FunctionExact valueDecimal
sin 195°−(√6 − √2)/4≈ −0.2588
cos 195°−(√6 + √2)/4≈ −0.9659
tan 195°2 − √3≈ 0.2679
cot 195°2 + √3≈ 3.7321

Reference angle: sin 15° = (√6 − √2)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
175°≈ 0.0872
179°≈ 0.0175
180°0
195°−(√6 − √2)/4
198°−(√5 − 1)/4
200°≈ −0.3420
210°−1/2

FAQ

What is sin 195°?

sin 195° = −(√6 − √2)/4 ≈ −0.2588

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show 0.2195 for sin 195?

The calculator is in radian mode (RAD): it takes sin 195 as the sine of 195 radians, sin 195 rad ≈ 0.2195. Switch it to degrees (DEG): sin 195° = −(√6 − √2)/4 ≈ −0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also