Trigonometric Ratios Triangles in Quadrant I

1. Trigonometric RatiosTriangles in Quadrant I

2. a Trig Ratio is … … a ratio of the lengths of two sides of a right Δ

3. 3 Basic Trig Ratios • Sine (sin) • Cosine (cos) • Tangent (tan) These trig ratios (or trig functions) can be used to SOLVE a right triangle … that means to find all the side lengths and angle measures of the right triangle.

4. Right Triangles • The hypotenuse is opposite the right angle. • The shortest side is opposite the smallest angle. • The longest side is opposite the largest angle. B hypotenuse a A b

5. Sinϴ= • Cosϴ = • Tanϴ=

6. Just remember Chief… SOHCAHTOA ine ppos i t e ypo t enuse osine d j acen t ypo t enuse angent ppos i t e d j acen t

7. Each trig function has a RECIPROCAL function. • sine → cosecant (csc) • cosine → secant (sec) • tangent → cotangent (cot)

8. Six Trig Ratios of ϴ r y ϴ x

9. Find the ratios for the 6 trig functions. sin ϴ = 5/13 cos ϴ = 12/13 tan ϴ = 5/12 csc ϴ = 13/5 sec ϴ = 13/12 cot ϴ = 12/5 13 5 ϴ 12

10. Find the ratios for the 6 trig functions. Given: cscϴ = 5/3 sin ϴ = 3/5 cos ϴ = 4/5 tan ϴ = 3/4 csc ϴ = 5/3 sec ϴ = 5/4 cot ϴ = 4/3 Use Pythagorean Theorem to find the missing side length! ϴ

11. Find the ratios for the 6 trig functions. Given: tanα = 4 sin α = cos α = tan α = 4 csc α = sec α = cot α = Use Pythagorean Theorem to find the missing side length! α