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Understanding Double-Angle and Half-Angle Identities in Trigonometry

This resource provides a comprehensive guide to Double-Angle and Half-Angle identities derived from sum identities. Explore examples that involve finding exact trigonometric values in various quadrants. The document also discusses projectile motion, illustrating how to calculate the horizontal distance traveled by a projectile based on initial velocity and launch angle. Homework exercises are included for practice. Perfect for students looking to strengthen their understanding of trigonometric identities and projectile motion concepts.

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Understanding Double-Angle and Half-Angle Identities in Trigonometry

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  1. 6.3 Double-Angle & Half-Angle Identities

  2. The Double-Angle Identities can be easily derived from the sum identities • • OR 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. 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 302 #1–19 odd, 24, 26, 27, 33, 41, 45, 47, 55

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