Tan 195 Degrees

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

What is tan 195°?

Answer

tan 195° =
2 − √3 ≈ 0.2679

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

≈ — rounded to 4 decimal places.

tan 195° = tan(180° + 15°) = tan 15° = 2 − √3

tan 195° = sin 195° / cos 195° = (−(√6 − √2)/4) / (−(√6 + √2)/4) = 2 − √3

tan 15° = tan(45° − 30°) = (1 − √3/3) / (1 + √3/3) = 2 − √3

xyOP

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

T(1, tan 195°) ≈ (1, 0.2679) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

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: tan 15° = 2 − √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
175°≈ −0.0875
179°≈ −0.0175
180°0
195°2 − √3
198°√(25 − 10√5)/5
200°≈ 0.3640
210°√3/3

FAQ

What is tan 195°?

tan 195° = 2 − √3 ≈ 0.2679

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 0.2249 for tan 195?

The calculator is in radian mode (RAD): it takes tan 195 as the tangent of 195 radians, tan 195 rad ≈ 0.2249. Switch it to degrees (DEG): tan 195° = 2 − √3 ≈ 0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also