Trigonometric Ratios and Their Inverses Def: Trigonometry is the study of relationships between sides of right triangles and their angle measurements.

The Sides in Relation to an Angle θ Opposite Hypotenuse Adjacent θ =is Greek for “Theta”

Now you try… Which side is opposite, adjacent, and the hypotenuse to give the angle? 1. Angle X 2. Angle Y f e d Y X Answer: Angle X-d=opposite, e=adjacent, f=hypotenuse Angle Y-e=opposite, d=adjacent, f=hypotenuse

3 Basic Trigonometric Ratios The Sine Ratio also known as sin θ Opp Hyp Adj 9 7 15

2. The Cosine Ratio also known as cos θ Opp Hyp Adj 9 7 15

3. The Tangent Ratio also known as tan θ Opp Hyp Adj 9 7 15

A Mnemonic Device

Using Trig to Find Missing Sides Example: Steps 1. Decide which trig ratio you need. A 7 m C B 56° 2. Write an equation 3. Use calculator to find trig value. 4. Cross multiply to solve the equation.

Now you try… Find the missing side: 1. 2. 3. z 4 cm 31° 27° a 10 cm b 15 m 48°

Inverse Trigonometry Sine, Cosine, and Tangent are used to find missing sides of a right triangle. The inverses of these ratios are used to find __________ of a right triangle. Notation: 1. Inverse Sine: or 2. Inverse Cosine: or 3. Inverse Tangent: or

Example: Steps 1. Decide which trig ratio you need. 2. Write an equation 3. Take the inverse of each side of the equation. 4. Use calculator to find inverse trig value. This value is the angle measurement.

Now you try… 1. Find angle R. 2. Find angle A. 3. Find θ Homework: C B 7 m 14 m 3. Find θ Homework: Pg. 624 #1-19