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Double-angle and half-angle identities, and verifying identities — Homework

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Double-angle and half-angle identities, and verifying identities — Homework

Find any missing side with the Pythagorean theorem first, and check the quadrant before choosing a half-angle sign.

  1. 1.Given cosA=5/13 with A in Quadrant I, find sin(2A) and cos(2A).
  2. 2.Find the exact value of sin(22.5 degrees) using the half-angle formula on 45 degrees.
  3. 3.Given sinA=-3/5 with A in Quadrant IV (so cosA=4/5), find sin(2A).
  4. 4.Verify the identity sin(2x)/(1+cos(2x)) = tan(x).
  5. 5.Explain why the half-angle formula for sine needs a plus-or-minus sign in front of the square root.
🌲 Homeschool of the FutureTwelfth Grade · Math · week 23 homework