Cos 195 Degrees

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

What is cos 195°?

Answer

cos 195° =
−(√6 + √2)/4 ≈ −0.9659

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

≈ — rounded to 4 decimal places.

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

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

cos 15° = cos(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 x-axis — cosine, x ≈ −0.9659.

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: cos 15° = (√6 + √2)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
175°≈ −0.9962
179°≈ −0.9998
180°−1
195°−(√6 + √2)/4
198°−√(10 + 2√5)/4
200°≈ −0.9397
210°−√3/2

FAQ

What is cos 195°?

cos 195° = −(√6 + √2)/4 ≈ −0.9659

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 0.9756 for cos 195?

The calculator is in radian mode (RAD): it takes cos 195 as the cosine of 195 radians, cos 195 rad ≈ 0.9756. Switch it to degrees (DEG): cos 195° = −(√6 + √2)/4 ≈ −0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also