Six Trigonometric Ratios

The six trigonometric ratios are: 1. Sine (sin) 2. Cosine (cos) 3. Tangent (tan) 4. Cosecant (csc) 5. Secant (sec) 6. Cotangent (cot)

Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: $$\text{sin} = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: $$\text{cos} = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side. Formula: $$\text{tan} = \frac{\text{opposite}}{\text{adjacent}}$$ .

Cosecant (csc) is the reciprocal of sine. Formula: $$\text{csc} = \frac{1}{\text{sin}} = \frac{\text{hypotenuse}}{\text{opposite}}$$ .

Secant (sec) is the reciprocal of cosine. Formula: $$\text{sec} = \frac{1}{\text{cos}} = \frac{\text{hypotenuse}}{\text{adjacent}}$$ .

Cotangent (cot) is the reciprocal of tangent. Formula: $$\text{cot} = \frac{1}{\text{tan}} = \frac{\text{adjacent}}{\text{opposite}}$$ .

The six trigonometric ratios are interrelated: 1. $$\text{csc} = \frac{1}{\text{sin}}$$ 2. $$\text{sec} = \frac{1}{\text{cos}}$$ 3. $$\text{cot} = \frac{1}{\text{tan}}$$ .

To find the sine of an angle, divide the length of the opposite side by the length of the hypotenuse: $$\text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$$ .

To find the cosine of an angle, divide the length of the adjacent side by the length of the hypotenuse: $$\text{cos}(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ .