Right Triangle Trigonometry

1. SOH CAH TOA CHO SHA CAO Right Triangle Trigonometry

2. Warm-up • Find the 6 trig function of θ = 13800

3. · the side adjacent · the side opposite opp hyp · and the hypotenuse adj θ The sides of the right triangle are: The trigonometric functions are CHO SHA CAO SOH CAH TOA

4. opp adj hyp sin θ = cos θ = tan θ = cot θ = sec θ = csc θ = 5 4 θ 3 Calculate the trigonometric functions for ∠θ . Example: The six trig ratios are

5. Calculate the trigonometric functions for a 30° angle. adj hyp opp adj hyp sin 30° = = 2 csc 30° = = = 2 sec 30° = = = cos 30° = = 1 cot 30° = = = tan 30° = = = opp adj hyp adj opp 30 Your Turn!

6. Cofunction Identities sin θ = cos(90°−θ) cos θ = sin(90°−θ)tan θ= cot(90°−θ) cot θ = tan(90°−θ)sec θ = csc(90°−θ) csc θ = sec(90°−θ) Reciprocal Identities sin θ = 1/csc θ cos θ = 1/sec θ tan θ = 1/cot θcot θ = 1/tan θ sec θ = 1/cos θ csc θ = 1/sin θ Quotient Identities tan θ = sin θ /cos θ cot θ = cos θ /sin θ Pythagorean Identities sin2 θ + cos2 θ = 1 tan2θ + 1 = sec2 θ cot2 θ + 1 = csc2 θ Fundamental Trigonometric Identities

7. Finding Values of Irregular angles sin 300 = .50 sin 950 = .99619 cos 1800 = .-1 cos 1090 = -.3257 sin 230 = .39073 tan 150 = .26795

8. 1 7 7 7 opp hyp opp hyp 1 = Sin 300 = = = 7 2 x x 30 Solve x: x 7 30 Sin 300 14 (2) x x = 14

9. x √2 7 7 7 14 x hyp adj hyp adj = 7 √2 √2 = cos 450 = = = = 7 2 x x 30 Your Turn Solve x: x 45 √2 √2 7 cos 45 7√2 x (2) √2

10. x x x x 12 √3 √3 adj opp = adj opp √3 = = tan 600 = = 12 12 Solve x: x 60 12 Tan 600 (12)