Tan 342 Degrees

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

What is tan 342°?

Answer

tan 342° =
−√(25 − 10√5)/5 ≈ −0.3249

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

≈ — rounded to 4 decimal places.

tan 342° = tan(360° − 18°) = −tan 18° = −√(25 − 10√5)/5

tan 342° = sin 342° / cos 342° = (−(√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 342°, sin 342°) ≈ (0.9511, −0.3090)

T(1, tan 342°) ≈ (1, −0.3249) — where line OP meets the line x = 1.

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: tan 18° = √(25 − 10√5)/5

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
324°−√(5 − 2√5)
330°−√3/3
341°≈ −0.3443
342°−√(25 − 10√5)/5
345°√3 − 2
355°≈ −0.0875
360°0

FAQ

What is tan 342°?

tan 342° = −√(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 −0.4630 for tan 342?

The calculator is in radian mode (RAD): it takes tan 342 as the tangent of 342 radians, tan 342 rad ≈ −0.4630. Switch it to degrees (DEG): tan 342° = −√(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