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**6.3 Double-Angle & Half-Angle Identities**

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

• OR

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**Double Angle Identities**

Half-Angle Identities

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**Examples: Find the exact values**

Ex 1) Find QII so (+)

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Ex 2) Given –5 θ –12 13

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

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**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 (+)

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**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?

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

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