1. 6.3 Double-Angle & Half-Angle Identities

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

3. Double Angle Identities
Half-Angle Identities

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

5. Ex 2) Given –5 θ
–12 13

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

7. 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 (+)

8. 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?

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