Tan 345 Degrees

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

What is tan 345°?

Answer

tan 345° =
√3 − 2 ≈ −0.2679

Angle in radians: 345° = 23π/12. The point of the angle is in quadrant IV, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 345° = tan(360° − 15°) = −tan 15° = √3 − 2

tan 345° = sin 345° / cos 345° = (−(√6 − √2)/4) / ((√6 + √2)/4) = √3 − 2

tan 15° = tan(45° − 30°) = (1 − √3/3) / (1 + √3/3) = 2 − √3

xyOP

P(cos 345°, sin 345°) ≈ (0.9659, −0.2588)

T(1, tan 345°) ≈ (1, −0.2679) — where line OP meets the line x = 1.

All four functions of 345°
FunctionExact valueDecimal
sin 345°−(√6 − √2)/4≈ −0.2588
cos 345°(√6 + √2)/4≈ 0.9659
tan 345°√3 − 2≈ −0.2679
cot 345°−2 − √3≈ −3.7321

Reference angle: tan 15° = 2 − √3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
330°−√3/3
341°≈ −0.3443
342°−√(25 − 10√5)/5
345°√3 − 2
355°≈ −0.0875
360°0
390°√3/3

FAQ

What is tan 345°?

tan 345° = √3 − 2 ≈ −0.2679

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show −0.6483 for tan 345?

The calculator is in radian mode (RAD): it takes tan 345 as the tangent of 345 radians, tan 345 rad ≈ −0.6483. Switch it to degrees (DEG): tan 345° = √3 − 2 ≈ −0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also