Tan 324 Degrees

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

What is tan 324°?

Answer

tan 324° =
−√(5 − 2√5) ≈ −0.7265

Angle in radians: 324° = 9π/5. The point of the angle is in quadrant IV, where tangent is negative.

≈ — rounded to 4 decimal places.

tan 324° = tan(360° − 36°) = −tan 36° = −√(5 − 2√5)

tan 324° = sin 324° / cos 324° = (−√(10 − 2√5)/4) / ((√5 + 1)/4) = −√(5 − 2√5)

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

tan 36° = sin 36° / cos 36° = √(5 − 2√5)

xyOP

P(cos 324°, sin 324°) ≈ (0.8090, −0.5878)

T(1, tan 324°) ≈ (1, −0.7265) — where line OP meets the line x = 1.

All four functions of 324°
FunctionExact valueDecimal
sin 324°−√(10 − 2√5)/4≈ −0.5878
cos 324°(√5 + 1)/4≈ 0.8090
tan 324°−√(5 − 2√5)≈ −0.7265
cot 324°−√(25 + 10√5)/5≈ −1.3764

Reference angle: tan 36° = √(5 − 2√5)

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
300°−√3
306°−√(25 + 10√5)/5
315°−1
324°−√(5 − 2√5)
330°−√3/3
341°≈ −0.3443
342°−√(25 − 10√5)/5

FAQ

What is tan 324°?

tan 324° = −√(5 − 2√5) ≈ −0.7265

How are sin 36° and cos 54° related?

They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

Why does a calculator show 0.4417 for tan 324?

The calculator is in radian mode (RAD): it takes tan 324 as the tangent of 324 radians, tan 324 rad ≈ 0.4417. Switch it to degrees (DEG): tan 324° = −√(5 − 2√5) ≈ −0.7265. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also