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

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

3. 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

4. 3 Basic Trigonometric Ratios
The Sine Ratio
also known as sin θ
Opp
Hyp
Adj 9 7 15

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

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

7. A Mnemonic Device

8. 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.

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

10. 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

11. 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.

12. 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