Tan 21 Degrees

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

What is tan 21°?

Answer

tan 21° ≈
0.3839

Angle in radians: 21° = 7π/60. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places. An exact form of tan 21° in square roots exists, but it is unwieldy — nested radicals.

tan 21° = sin 21° / cos 21° ≈ 0.3839

xyOP

P(cos 21°, sin 21°) ≈ (0.9336, 0.3584)

T(1, tan 21°) ≈ (1, 0.3839) — where line OP meets the line x = 1.

All four functions of 21°
FunctionExact valueDecimal
sin 21°—≈ 0.3584
cos 21°—≈ 0.9336
tan 21°—≈ 0.3839
cot 21°—≈ 2.6051

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
18°√(25 − 10√5)/5
19°≈ 0.3443
20°≈ 0.3640
21°≈ 0.3839
22°≈ 0.4040
23°≈ 0.4245
24°≈ 0.4452

FAQ

What is tan 21°?

tan 21° ≈ 0.3839

Is there an exact value of tan 21°?

Yes: 21° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: tan 21° ≈ 0.3839.

Why does a calculator show −1.5275 for tan 21?

The calculator is in radian mode (RAD): it takes tan 21 as the tangent of 21 radians, tan 21 rad ≈ −1.5275. Switch it to degrees (DEG): tan 21° ≈ 0.3839. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also