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Right-angled trig (SOH CAH TOA) formula

The right-angled trig (soh cah toa) formula as it is used in GCSE Mathematics, taken from the GCSE Mathematics formula sheet.

The formula

sin⁡θ=OH,cos⁡θ=AH,tan⁡θ=OA\sin\theta = \dfrac{O}{H}, \quad \cos\theta = \dfrac{A}{H}, \quad \tan\theta = \dfrac{O}{A}

How to use it in the exam

  • Write the formula down before substituting — most mark schemes award a method mark for a correct, clearly quoted formula.
  • Check every quantity is in consistent units before you substitute, then substitute in one step so the working stays easy to follow.
  • Show the rearrangement rather than jumping to the answer, and give the final value to the accuracy the question asks for.

Related pythagoras & trigonometry formulas

Pythagoras' theorem
a2+b2=c2a^2 + b^2 = c^2
Sine rule
asin⁡A=bsin⁡B=csin⁡C\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}
Cosine rule
a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc\cos A
Area of a triangle
A=12absin⁡CA = \tfrac{1}{2}ab\sin C

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