CHAPTER 4TRIGONOMETRIC FUNCTIONS

Section 3

Right Triangle Trigonometry

THE RIGHT TRIANGLE

The Six Trigonometric Functions

1. Sine (sin)

2. Cosecant (csc)

3. Cosine (cos)

4. Secant (sec)

5. Tangent (tan)

6. Cotangent (cot)

Right Triangle Definitions of Trigonometric Functions

sin θ = opp/hypcos θ = adj/hyptan θ =opp/adj

csc θ = hyp/oppsec θ = hyp/adjcot θ =adj/opp

Example #1 (Booyakasha!)

SOLUTIONSOLUTION

By the Pythagorean Theorem,

(hyp)^2 = (opp)^2 + (adj)^2

hyp =

sin θ = opp/hyp = 12/15 = 4/5

csc θ = hyp/opp = 5/4

cos θ = adj/hyp = 3/5

sec θ = hyp/adj = 5/3

tan θ = opp/adj = 4/3

cot θ = adj/opp = 3/4

Do it yourself!

Solve for the missing side using the Pythagorean Theorem. Then find the six trigonometric functions.