SOHCAHTOA: the sine, cosine and tangent ratios

\sin\theta = \dfrac{\text{opp}}{\text{hyp}}\quad \cos\theta = \dfrac{\text{adj}}{\text{hyp}}\quad \tan\theta = \dfrac{\text{opp}}{\text{adj}}

SOHCAHTOA is the mnemonic for the three ratios in a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent. Everything else in trigonometry is built on these three. Use it whenever a problem gives you a right angle and any two of a side, an angle, or the hypotenuse.

right trianglebasic

Related Basics identities

Degrees ↔ radians Arc length Sector area

Common questions

What is the SOHCAHTOA identity?

When do you use the SOHCAHTOA identity?

Use it whenever a problem gives you a right angle and any two of a side, an angle, or the hypotenuse.

Which identities are related to SOHCAHTOA?

SOHCAHTOA belongs to the Basics group. The identities used alongside it most often are Degrees ↔ radians, Arc length and Sector area.

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Basics questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Practise Basics Open the triangle solver

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.