1. 5.2 Trig Ratios in Right Triangles
Objective: Find the values of trig ratios for acute angles of right triangles.

2. 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.

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

4. Reciprocal Trig Ratios:
Ex. 1)
Find the values of the sine, cosine, and tangent for <A. C 8 B 15 A
90°
Reciprocal Trig Ratios:
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.)

5. a.) If sec θ = 6/5 , find cos θ. b.) If sin θ = 0.8, find csc θ.
Ex. 2)
a.) If sec θ = 6/5 , find cos θ. b.) If sin θ = 0.8, find csc θ.
Ex. 3)
Find the values of the six trig ratios for <E. D
3cm E
F (90°)
7 cm

6. 45°-45°-90°
45°
x x√2
45°
90° x
30°-60°-90°
30° 2x
x√3
60°
90° x

7. sin θ = cos(90° - θ ) cos θ = sin (90°- θ )
Tanθ
cscθ
secθ
cotanθ
30°
1/2
√3/2
√3/3 2
2√3/3 √3
45°
√2/2 1 √2
60°
Cofunctions:
(When θ is acute)
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)