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6.3 Double-Angle & Half-Angle Identities. The Double-Angle Identities can be easily derived from the sum identities OR.

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Presentation on theme: "6.3 Double-Angle & Half-Angle Identities. The Double-Angle Identities can be easily derived from the sum identities OR."— Presentation transcript:

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 13 θ –12

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

7 Ex 4) Given 1 2 sec (recip of cos) is (+) in QI & QIV tan is (–) in QII & QIV 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/s 2 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 302 #1–19 odd, 24, 26, 27, 33, 41, 45, 47, 55


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