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Chapter 7

Chapter 7. Analytic Trigonometry. Section 5 Double Angle and Half Angle Formulas. Double Angle Formulas. This is another way of evaluating exact answers of trig functions  strictly for angles not on the unit circle. sin(2 ) = 2sin cos c os(2 ) = cos 2 - sin 2 c os(2 ) = 1 – 2sin 2

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Chapter 7

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  1. Chapter 7 Analytic Trigonometry

  2. Section 5Double Angle and Half Angle Formulas

  3. Double Angle Formulas

  4. This is another way of evaluating exact answers of trig functions  strictly for angles not on the unit circle

  5. sin(2) = 2sincos cos(2) = cos2 - sin2 cos(2) = 1 – 2sin2 cos(2) = 2cos2 - 1 tan(2) = *these are on pages 476-477

  6. *Reason that these only apply to non-unit circle values: 2 of anything on the unit circle would be an angle on the unit circle, making the formulas pointless

  7. Example 1: Find sin(2), cos(2), and tan(2) IF sin = 3/5 and < < sin(2)

  8. Example 1: (continued) cos(2) tan(2)

  9. Example 2: Find sin(2), cos(2), and tan(2) IF cot = -2, sec < 0 sin(2)

  10. Example 2: (continued) cos(2) tan(2)

  11. Half Angle Formulas

  12. *These formulas, like the sum and difference formulas, can be used with actual unit circle values or unknown angles and triangles.

  13. *You will need to choose + or -, it is NOT both!! *these are on page 480

  14. When given real numbers: 1 - Decide which quadrant the given angle would fall in (this will tell you whether the answer should be + or -) 2 - Multiply the given angle by 2 (this shows which unit circle value /2 would give you the given angle) 3 - Use the appropriate formula with the angle from #2 to find an exact answer

  15. Example 1: sin(15*)

  16. Example 2: cos(337.5*)

  17. Example 3: tan()

  18. When given a description: 1 – draw a triangle and list sin and cos 2 – determine which quadrant ½ the angle would be in 3 – use formula to find exact value

  19. Example 4: If tan = ¾, < < , find sin/2, cos /2, and tan /2. sin/2

  20. Example 4: (continued) cos /2 tan /2

  21. EXIT SLIP

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