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SOH CAH TOA. CHO SHA CAO. Right Triangle Trigonometry. Warm-up. Find the 6 trig function of. θ = 1380 0. · 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.
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SOH CAH TOA CHO SHA CAO Right Triangle Trigonometry
Warm-up • Find the 6 trig function of θ = 13800
· 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
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
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!
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
Finding Values of Irregular angles sin 300 = .50 sin 950 = .99619 cos 1800 = .-1 cos 1090 = -.3257 sin 230 = .39073 tan 150 = .26795
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
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
x x x x 12 √3 √3 adj opp = adj opp √3 = = tan 600 = = 12 12 Solve x: x 60 12 Tan 600 (12)