1. 13.1 Right Triangle Trigonometry

2. Definition  A right triangle with acute angle θ, has three sides referenced by angle θ. These sides are opposite θ, adjacent to θ, and the hypotenuse. θ hypotenuse (hyp) opposite side (opp) adjacent side (adj)

3. Definition  The six different ways these sides can be arranged into ratios define the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. θ hypotenuse (hyp) opposite side (opp) adjacent side (adj) These functions are abbreviated sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ

4. Trigonometric Functions

5. Definition  Note that the ratios in the second column are the reciprocals of the ratios in the first column.

6. θ (hyp) = 2 (opp) = 1 (adj) = For a given triangle with angle θ equal to 30˚, the opposite side is equal to a length of 1, the hypotenuse is equal to 2, and the adjacent side is equal to. Find the six trig ratios.

7. (hyp) = 2 (opp) = (adj) = 1 If the same triangle is rotated and we examine θ as the 60˚ angle, find the new trig ratios. θ

8. (hyp) = (opp) = 1 (adj) = 1 If we now examine θ as a 45˚ angle, the measurement of the sides changes as displayed in the figure. Find the trig ratios for a 45˚ angle. θ

9. Memory option 1 (hyp) = 2 (opp) = 1 (adj) = (hyp) = (opp) = 1 (adj) = 1 45˚30˚ 60˚ 45˚

10. Memory option 2 θsin θcos θtan θcsc θsec θcot θ 30˚½/2/32 45˚/2 11 60˚/2½ /32