Theory

Note that Trigonometry also only holds for right angle triangle.

Useful terms:

            hypotenuse: longest side of right angle triangle, directly opposite to the right angle

            opposite side: directly opposite of the chosen angle θ

            adjacent side: the adjacent side of the chosen angle θ

Note that opposite sides and adjacent sides change with respect to the chosen angle θ.

Study the diagram carefully. Make sure you understand what each sides are called.

Then, trigonometry tells you that:

sine θ or sin θ = opposite / hypotenuse

cosine θ or cos θ = adjacent / hypotenuse

tangent θ or tan θ = opposite / adjacent

In order to memorise these easily, we first simplify by taking first letter of each, thus:

sin θ = O / H

cos θ = A / H

tan θ = O / A

Then we can memorise the first letters of each equation and say

SOH CAH TOA

To find the angle:

If we are trying to calculate the angle A given the values of sides then we can use the inverses of sine cosine and tangent.

sin θ = O / H

inverse of sine or arcsin O / H = θ

inverse of cosine or arccos A / H = θ

inverse of tangent or arctan O / A = θ 

Please also note that in your calculator, inverse of sin cos and tan are shown as sin^-1, cos^-1 and tan^-1