Trigonometric Ratios in Right Triangles: An Introductory Guide

1. The opposite and adjacent sides change depending on which acute angle you use. There are 6 trig ratios that can be formed from the acute angle θ. Sine θ = sin θ Cosecant θ = cscθ Cosine θ = cosθ Secant θ = sec θ Tangent θ = tan θ Cotangent θ = cot θ hypotenuse hypotenuse θ opposite adjacent θ adjacent opposite

2. If we know 2 sides of a right triangle how can we find the third side? Pythagorean theorem: leg2 + leg2 = hypotnuse2 Example: 4 8 11 6 h2 = 42 + 62 l2 + 82 = 112 h2 = 16 + 36 l2 + 64 = 121 h2 = 52 l2 = 57 h = √52 l = √57 h = 2√13

3. Lets combine the two slides If we know all 3 sides of a right triangle we can find the ratio that each trig function. Lets take the first example: 2√13 ø from whichever angle is marked we can state the 6 trig ratios. Sin ø = 4/2√13 = 2/√13 Cos ø = 6/2√13 = 3/√13 Tan ø = 4/6 = 2/3 Cscø = 2√13/4 = √13/2 Sec ø = 2√13/6 = √13/3 Cot ø = 6/4 = 3/2

4. Homework assignment # 1 Pg. 516 (9-18 all)