Tan 75 Degrees

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

What is tan 75°?

Answer

tan 75° =
2 + √3 ≈ 3.7321

Angle in radians: 75° = 5π/12. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 75° = sin 75° / cos 75° = ((√6 + √2)/4) / ((√6 − √2)/4) = 2 + √3

tan 75° = tan(45° + 30°) = (1 + √3/3) / (1 − √3/3) = 2 + √3

xyOP

P(cos 75°, sin 75°) ≈ (0.2588, 0.9659)

T(1, tan 75°) ≈ (1, 3.7321) — where line OP meets the line x = 1; T is beyond the drawing, the arrow points to it.

All four functions of 75°
FunctionExact valueDecimal
sin 75°(√6 + √2)/4≈ 0.9659
cos 75°(√6 − √2)/4≈ 0.2588
tan 75°2 + √3≈ 3.7321
cot 75°2 − √3≈ 0.2679

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
72°√(5 + 2√5)
73°≈ 3.2709
74°≈ 3.4874
75°2 + √3
76°≈ 4.0108
77°≈ 4.3315
78°≈ 4.7046

FAQ

What is tan 75°?

tan 75° = 2 + √3 ≈ 3.7321

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 −0.4207 for tan 75?

The calculator is in radian mode (RAD): it takes tan 75 as the tangent of 75 radians, tan 75 rad ≈ −0.4207. Switch it to degrees (DEG): tan 75° = 2 + √3 ≈ 3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also