1. Trigonometric Ratios Triangles 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. A b a B

5. Sin = Cos = Tan =

6. Just remember Chief… SOHCAHTOA ineine ppositepposite ypotenuseypotenuse osineosine djacentdjacent ypotenuseypotenuse angentangent ppositepposite djacentdjacent

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

8. Six Trig Ratios of  Six Trig Ratios of  x y r

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

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

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