Tan 225 Degrees

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

What is tan 225°?

Answer

tan 225° =
1

Angle in radians: 225° = 5π/4. The point of the angle is in quadrant III, where tangent is positive.

tan 225° = tan(180° + 45°) = tan 45° = 1

tan 225° = sin 225° / cos 225° = (−√2/2) / (−√2/2) = 1

An isosceles right triangle with legs 1: the hypotenuse is √2.

tan 45° = 1/1 = 1

xyOP

P(cos 225°, sin 225°) ≈ (−0.7071, −0.7071)

T(1, tan 225°) = (1, 1) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

All four functions of 225°
FunctionExact valueDecimal
sin 225°−√2/2≈ −0.7071
cos 225°−√2/2≈ −0.7071
tan 225°11
cot 225°11

Reference angle: tan 45° = 1

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
211°≈ 0.6009
215°≈ 0.7002
216°√(5 − 2√5)
225°1
227°≈ 1.0724
234°√(25 + 10√5)/5
240°√3

FAQ

What is tan 225°?

tan 225° = 1

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: tan 225° = 1.

Why does a calculator show −2.5321 for tan 225?

The calculator is in radian mode (RAD): it takes tan 225 as the tangent of 225 radians, tan 225 rad ≈ −2.5321. Switch it to degrees (DEG): tan 225° = 1. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also