# Trigonometry- Sin, Cos, Tan

## Trigonometry- Sin, Cos, Tan

# Trigonometric Ratios

**Trigonometry**deals with the relationship between the angles and sides of a triangle.- It’s most commonly used with right-angled triangles, where one angle is 90 degrees.

## Definitions and Ratios

- The three main trigonometric ratios are:
**sine (sin)**,**cosine (cos)**, and**tangent (tan)**. - In any right-angle triangle, the
**hypotenuse**is the longest side opposite the right angle, the**opposite**is the side opposite the angle under consideration, and the**adjacent**is the side lying next to (or adjoining) the angle under consideration. **Sine**of an angle (θ) is calculated as the ratio of the length of the side**opposite**the angle (O) to the length of the**hypotenuse**(H): sin θ = O/H.**Cosine**of an angle (θ) is calculated as the ratio of the length of the**adjacent**side (A) to the length of the**hypotenuse**(H): cos θ = A/H.**Tangent**of an angle (θ) is calculated as the ratio of the**opposite**side (O) to the**adjacent**side (A): tan θ = O/A.

## The Sine Rule and Cosine Rule

**The Sine Rule**states that the ratio of a side of a triangle to the sine of its opposite angle is the same for all three sides. It helps you to find missing sides/angles in a triangle if you know one angle and two sides, or two angles and one side.**The Cosine Rule**relates the lengths of the sides of a triangle to the cosine of one of the angles. Use the Cosine Rule when you know the lengths of two sides and the size of the enclosed angle, or the lengths of three sides and you want to find one of the angles.

## Simple Trigonometric Equations

**Trigonometric equations**typically involve the unknown number being inside the trigonometric function (like`sin x = 0.5`

), meaning you need to manipulate the equation a bit differently.- You can solve
**trigonometric equations**by using graphs and exact values, using trigonometric identities, or using the ‘CAST’ diagram.