6.3 Double-Angle & Half-Angle Identities

The Double-Angle Identities can be easily derived from the sum identities • OR

Double Angle Identities Half-Angle Identities

Examples: Find the exact values Ex 1) Find  QII so (+)

Ex 2) Given –5 θ –12 13

Ex 3) Given Is it (+) or (–)? 4  –3 5  QII so cos is (–)

sec (recip of cos) is (+) in QI & QIV tan is (–) in QII & QIV Ex 4) Given sec (recip of cos) is (+) in QI & QIV tan is (–) in QII & QIV 1  2  QII so sin is (+)

The horizontal distance a projectile can travel can be found using where v = initial velocity θ = launch angle g = gravitational constant = 9.8 m/s2 Ex 5) A punter consistently kicks the football at a 42° angle with an initial velocity of 25 m/s. How far from the punter is the ball when it hits the ground?

Homework #602 Pg 302 #1–19 odd, 24, 26, 27, 33, 41, 45, 47, 55