CHAPTER 4 TRIGONOMETRIC FUNCTIONS Jungeun Park Reem Malak MARY OGUNKORODE CHAPTER 4 TRIGONOMETRIC FUNCTIONS Section 3 Right Triangle Trigonometry

THE RIGHT TRIANGLE Hypotenuse Opposite to θ ( θ Adjacent to θ

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/hyp cos θ = adj/hyp tan θ =opp/adj csc θ = hyp/opp sec θ = hyp/adj cot θ =adj/opp

Example #1 (Booyakasha!) SOLUTION 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 Hypotenuse 12 θ 9

Do it yourself! Solve for the missing side using the Pythagorean Theorem. Then find the six trigonometric functions. 25 20