Finite Trig Ratios

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is represented as $$\frac{adjacent}{hypotenuse}$$ .

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. It is represented as $$\frac{opposite}{hypotenuse}$$ .

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It is represented as $$\frac{opposite}{adjacent}$$ .

$$\tan A = \frac{\text{sine A}}{\text{cosine A}} = \frac{\frac{opposite}{hypotenuse}}{\frac{adjacent}{hypotenuse}} = \frac{opposite}{adjacent}$$ .

$$\frac{adjacent}{hypotenuse} = \frac{21}{29}$$ .

$$\frac{opposite}{hypotenuse} = \frac{20}{29}$$ .

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

$$\text{cosine}(45^\text{o}) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{1}{\frac{\text{sqrt}(2)}{2}} = \frac{\text{sqrt}(2)}{2}$$ .

The sides of a right triangle are proportional to the sine and cosine of its angles. For angle A, $$\frac{opposite}{hypotenuse} = \text{sine A}$$ and $$\frac{adjacent}{hypotenuse} = \text{cosine A}$$ .

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It is expressed as $$a^2 + b^2 = c^2$$ .