Cos 342 Degrees

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

What is cos 342°?

Answer

cos 342° =
√(10 + 2√5)/4 ≈ 0.9511

Angle in radians: 342° = 19π/10. The point of the angle is in quadrant IV, where cosine is positive.

≈ — rounded to 4 decimal places.

cos 342° = cos(360° − 18°) = cos 18° = √(10 + 2√5)/4

P(cos 342°, sin 342°) = (√(10 + 2√5)/4, −(√5 − 1)/4)

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

cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

xyOP

P(cos 342°, sin 342°) ≈ (0.9511, −0.3090)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.9511.

All four functions of 342°
FunctionExact valueDecimal
sin 342°−(√5 − 1)/4≈ −0.3090
cos 342°√(10 + 2√5)/4≈ 0.9511
tan 342°−√(25 − 10√5)/5≈ −0.3249
cot 342°−√(5 + 2√5)≈ −3.0777

Reference angle: cos 18° = √(10 + 2√5)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
324°(√5 + 1)/4
330°√3/2
341°≈ 0.9455
342°√(10 + 2√5)/4
345°(√6 + √2)/4
355°≈ 0.9962
360°1

FAQ

What is cos 342°?

cos 342° = √(10 + 2√5)/4 ≈ 0.9511

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 −0.9075 for cos 342?

The calculator is in radian mode (RAD): it takes cos 342 as the cosine of 342 radians, cos 342 rad ≈ −0.9075. Switch it to degrees (DEG): cos 342° = √(10 + 2√5)/4 ≈ 0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also