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Essential Question: How do I use trig identities to solve equations and verify identities?

Essential Question: How do I use trig identities to solve equations and verify identities?. How do I use the double angle and half angle formulas?. Double Angle Formulas. sin 2 . = 2 sin  cos . cos 2 . = cos 2  - sin 2 . = 2cos 2  - 1. = 1 – 2 sin 2 . tan 2  =. Ex. 1.

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Essential Question: How do I use trig identities to solve equations and verify identities?

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  1. Essential Question: How do I use trig identities to solve equations and verify identities? How do I use the double angle and half angle formulas?

  2. Double Angle Formulas sin 2 = 2 sin  cos  cos 2 = cos2 - sin2 = 2cos2 - 1 = 1 – 2 sin2 tan 2 =

  3. Ex. 1 Use the following to find sin2, cos2 and tan2 5 -12 13

  4. Ex. 1 5 -12 13 Use the following to find sin2, cos2 and tan2

  5. Ex. 1 5 -12 13 Use the following to find sin2, cos2 and tan2

  6. Ex. 2 and  terminates in the first quadrant, find the exact value of sin2, cos2 and tan 2. 5 You Try!!

  7. What are your questions??

  8. Half-Angle Identities

  9. Half-Angle Identities

  10. Example: Finding an Exact Value • Find the exact value of sin (/8).

  11. Example: Finding an Exact Value • Find the exact value of tan 22.5 using the identity • Since 22.5 = replace A with 45.

  12. Example: Finding an Exact Value continued • Multiply the numerator and denominator by 2, than rationalize the denominator.

  13. Example: Verifying identities Verify that 1 – cos 2x sec2x = tan2x is an identity.

  14. Simplify: Solution: Example: Simplifying Expressions

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