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8

Trigonometry Notes

TRIGONOMETRY: TRIGONOMETRIC RATIO:

S O H - C A H - T O A

* ϴ = any acute angle in a right triangle

Example 1 Express each ratio as a fraction in simplest form and as a decimal to the nearest hundredth a) Sin P d) Cos P b) Tan P e) Sin Q c) Cos Q f) Tan Q

SOH-CAH-TOA

Sine

Cosine

Tangent

A

B C a

c

R

Q

15

17

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tan opposite Tana a tanB badjacent b a

gC

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1.88 8 20.4717

1,4 0.88 185 0.53

Example 2 Find each ratio as a fraction in simplest form and as a decimal to the nearest hundredth a) sin J b) cos J c) tan J d) sin K e) cos K f) tan K Example 3 Example 4 Find x to the nearest hundredth Find x to the nearest hundredth

InverSe TrIg rATIOS

x Inverse sine x Inverse cosine x Inverse tangent

K

J L

13 5

12

SOH CAH TOA

5,3 0.38 92

72 041 1,13 0.925 38 3 2.413

Scott CAH

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tf CosA X then cos X mcA

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Examples Use a calculator to find m∠A to the nearest tenth 1. 2. 3. 4.

A B tanA

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A sin Ya cC A

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SOLVING RIGHT TRIANGLES

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Special Right 1 SIDE AND

Triangle 1 ANGLE 2 SIDESl I I r r

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use triangle sum theorem tofind missing angle All Ls addupto

1800