Sin 198 Degrees

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

What is sin 198°?

Answer

sin 198° =
−(√5 − 1)/4 ≈ −0.3090

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

≈ — rounded to 4 decimal places.

sin 198° = sin(180° + 18°) = −sin 18° = −(√5 − 1)/4

P(cos 198°, sin 198°) = (−√(10 + 2√5)/4, −(√5 − 1)/4)

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

sin 18° = cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

xyOP

P(cos 198°, sin 198°) ≈ (−0.9511, −0.3090)

Highlighted: the projection on the y-axis — sine, y ≈ −0.3090.

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: sin 18° = (√5 − 1)/4

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
179°≈ 0.0175
180°0
195°−(√6 − √2)/4
198°−(√5 − 1)/4
200°≈ −0.3420
210°−1/2
211°≈ −0.5150

FAQ

What is sin 198°?

sin 198° = −(√5 − 1)/4 ≈ −0.3090

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 −0.0796 for sin 198?

The calculator is in radian mode (RAD): it takes sin 198 as the sine of 198 radians, sin 198 rad ≈ −0.0796. Switch it to degrees (DEG): sin 198° = −(√5 − 1)/4 ≈ −0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also