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6.3 Double-Angle & Half-Angle Identities

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Presentation on theme: "6.3 Double-Angle & Half-Angle Identities"— 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 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


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