1. 8.4
Trigonometric Ratios

2. Background
The word trigonometry comes from two Greek terms, trigon (triangle) and metron (measure).
A trigonometric ratio is a ratio of the lengths of two sides of a RIGHT triangle.
The trig ratios stay constant for any size triangle with the same angle measures.

3. The Trig Ratios
Sine (written as sin θ)- the ratio of the side opposite θ to the hypotenuse.
Cosine(cos θ)- the ratio of the side adjacent to θ to the hypotenuse
Tangent(tan θ)– the ratio of the side opposite θ to the side adjacent to θ

4. And to remember this…
SOH –CAH – TOA

5. Example 1
Express each ratio as a fraction and a decimal to the nearest hundredth.
A. sin L
B. cos L
C. tan L
D. sin N
E. cos N
F. tan N

6. Assignment
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7. Example 2
Use a special right triangle to express the cosine of 60˚ as a fraction and a decimal to the nearest hundredth.

8. Example 3
Find y.

9. Example 4
Find x.

10. Inverse Trig Functions
sin-1
cos-1
tan-1
These are used whenever you need to get rid of a trig function to find the measure of an angle.

11. Example 5
Use a calculator to find the measure of angle P to the nearest tenth.

12. Example 6
Find the measures of the angles.

13. Assignment
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