Tan 162 Degrees

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

What is tan 162°?

Answer

tan 162° =
−√(25 − 10√5)/5 ≈ −0.3249

Angle in radians: 162° = 9π/10. The point of the angle is in quadrant II, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 162° = tan(180° − 18°) = −tan 18° = −√(25 − 10√5)/5

tan 162° = sin 162° / cos 162° = ((√5 − 1)/4) / (−√(10 + 2√5)/4) = −√(25 − 10√5)/5

Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

tan 18° = sin 18° / cos 18° = √(25 − 10√5)/5

xyOP

P(cos 162°, sin 162°) ≈ (−0.9511, 0.3090)

T(1, tan 162°) ≈ (1, −0.3249) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 162°
FunctionExact valueDecimal
sin 162°(√5 − 1)/4≈ 0.3090
cos 162°−√(10 + 2√5)/4≈ −0.9511
tan 162°−√(25 − 10√5)/5≈ −0.3249
cot 162°−√(5 + 2√5)≈ −3.0777

Reference angle: tan 18° = √(25 − 10√5)/5

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
150°−√3/3
159°≈ −0.3839
160°≈ −0.3640
162°−√(25 − 10√5)/5
164°≈ −0.2867
165°√3 − 2
167°≈ −0.2309

FAQ

What is tan 162°?

tan 162° = −√(25 − 10√5)/5 ≈ −0.3249

How are sin 18° and cos 72° related?

They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

Why does a calculator show −4.7387 for tan 162?

The calculator is in radian mode (RAD): it takes tan 162 as the tangent of 162 radians, tan 162 rad ≈ −4.7387. Switch it to degrees (DEG): tan 162° = −√(25 − 10√5)/5 ≈ −0.3249. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also