SOH CAH TOA Right Triangle Trigonometry CHO SHA

SOH CAH TOA Right Triangle Trigonometry CHO SHA CAO

Warm-up Find the 6 trig function of θ = 0 1380

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

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

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

Fundamental Trigonometric Identities 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 cot θ = 1/tan θ cos θ = 1/sec θ = 1/cos θ tan θ = 1/cot θ csc θ = 1/sin θ Quotient Identities tan θ = sin θ /cos θ cot θ = cos θ /sin θ Pythagorean Identities sin 2 θ + cos 2 θ = 1 tan 2 θ + 1 = sec 2 θ cot 2 θ + 1 = csc 2 θ

Finding Values of Irregular angles sin 0 30 cos 1800 =. 50 =. -1 sin 230 =. 39073 0 15 =. 26795 tan sin cos 0 95 0 109 =. 99619 = -. 3257

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

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

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