5 2 Trig Ratios in Right Triangles Objective

5. 2 Trig Ratios in Right Triangles Objective: Find the values of trig ratios for acute angles of right triangles.

Jokes of the day! What does a nosy pepper do? He gets jalapeno business. What did the Indian chief say to his wife who had sore feet? soh-cah-toa! What did the right triangle say to the priest in the confession booth? Father forgive me, for I have sined.

A Parts of a right triangle: b 90° C c a *SOH – CAH – TOA* -sides a and b are legs. -side c is the hypotenuse -side b is opposite <B -side a is adjacent to <B B sine = opp. cosine = adj. tangent = opp. hyp. adj.

Ex. 1) Find the values of the sine, cosine, and tangent for <A. C 8 90° Reciprocal Trig Ratios: B 15 A cosecant θ (csc θ) = 1/sin θ (hyp. /opp. ) secant θ (sec θ) = 1/cos θ (hyp. /adj. ) cotangent θ (cot θ) = 1/tan θ (adj. /opp. )

Ex. 2) Ex. 3) a. ) If sec θ = 6/5 , find cos θ. b. ) If sin θ = 0. 8, find csc θ. Find the values of the six trig ratios for <E. D 3 cm E 7 cm F (90°)

45° 45°-90° x√ 2 45° x 30°-60°-90° 2 x x√ 3 90° x 60°

θ Sinθ Cosθ Tanθ cscθ secθ cotanθ 30° 1/2 √ 3/3 2 2√ 3/3 √ 3 45° √ 2/2 1 √ 2 1 60° √ 3/2 1/2 √ 3 2√ 3/3 2 √ 3/3 Cofunctions: sin θ = cos(90° - θ ) tan θ = cot(90°- θ ) (When θ is sec θ = csc(90°- θ) acute) cos θ = sin (90°- θ ) cot θ = tan(90°- θ ) csc θ = sec(90°- θ)