5.2 Trigonometric Ratios in Right Triangles

A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called the hypotenuse, and the remaining two sides are called the legs of the triangle. c b a

Initial side Terminal side

The six ratios of a right triangle are called trigonometric functions of acute angles and are defined as follows: Function nameAbbreviationValue

Find the value of each of the six trigonometric functions of the angle Adjacent c = Hypotenuse = 13 b = Opposite = 12

Reciprocal Identities

FIND THE VALUE OF THE RECIPROCAL FUNCTION: 1.sin s = 3/5 2.cos s = 4/5 3. cot s = - ½ FIND ALL REMAINING TRIG FUNCTIONS IF sin s = 3/5 FIND ALL 6 TRIG FUNCTION VALUES IF s = 3  4

Let’s go over those special right Triangles:

 Sin  Cos  Tan  0  6 Or 30 degrees  4 Or 45 degrees  3 Or 60 degrees