8.4Trigonometric Ratios

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.

Background

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

The Trig Ratios

SOH –CAH – TOA

And to remember this…

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

Example 1

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Assignment

Use a special right triangle to express the cosine of 60˚ as a fraction and a decimal to the nearest hundredth.

Example 2

Find y.

Example 3

Find x.

Example 4

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.

Inverse Trig Functions

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

Example 5

Find the measures of the angles.

Example 6

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Assignment