Tan 198 Degrees

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

What is tan 198°?

Answer

tan 198° =
√(25 − 10√5)/5 ≈ 0.3249

Angle in radians: 198° = 11π/10. The point of the angle is in quadrant III, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 198° = tan(180° + 18°) = tan 18° = √(25 − 10√5)/5

tan 198° = sin 198° / cos 198° = (−(√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 198°, sin 198°) ≈ (−0.9511, −0.3090)

T(1, tan 198°) ≈ (1, 0.3249) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 198°
FunctionExact valueDecimal
sin 198°−(√5 − 1)/4≈ −0.3090
cos 198°−√(10 + 2√5)/4≈ −0.9511
tan 198°√(25 − 10√5)/5≈ 0.3249
cot 198°√(5 + 2√5)≈ 3.0777

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

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
179°≈ −0.0175
180°0
195°2 − √3
198°√(25 − 10√5)/5
200°≈ 0.3640
210°√3/3
211°≈ 0.6009

FAQ

What is tan 198°?

tan 198° = √(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 0.0798 for tan 198?

The calculator is in radian mode (RAD): it takes tan 198 as the tangent of 198 radians, tan 198 rad ≈ 0.0798. Switch it to degrees (DEG): tan 198° = √(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