SOHCAHTOA

SOHCAHTOA is a mnemonic to remember the definitions of the sine, cosine, and tangent functions in a right triangle: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

The hypotenuse is the side opposite the right angle and is the longest side of a right triangle.

The formula for sine is: $$\text{sin}(x) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

The formula for cosine is: $$\text{cos}(x) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

The formula for tangent is: $$\text{tan}(x) = \frac{\text{opposite}}{\text{adjacent}}$$ .

$$\text{sin}(x) = \frac{4}{5} = 0.8$$ .

$$\text{cos}(x) = \frac{3}{5} = 0.6$$ .

$$\text{tan}(x) = \frac{4}{3} \text{ or approximately } 1.33$$ .

The Pythagorean theorem states that: $$a^2 + b^2 = c^2$$ , where c is the hypotenuse and a and b are the other two sides.

$$\text{sin}(30^\text{o}) = \frac{1}{2}$$ .