1. Right Triangle Trigonometry
SOH CAH TOA
CHO SHA CAO

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

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

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

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

6. 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 cos θ = 1/sec θ tan θ = 1/cot θ cot 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 tan2 θ + 1 = sec2 θ cot2 θ + 1 = csc2 θ

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

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

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

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