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DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

DOUBLE-ANGLE AND HALF-ANGLE FORMULAS. If we want to know a formula for we could use the sum formula. we can trade these pla ces. This is called the double angle formula for sine since it tells you the sine of double . Let's try the same thing for.

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DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

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  1. DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

  2. If we want to know a formula for we could use the sum formula. we can trade these places This is called the double angle formula for sine since it tells you the sine of double 

  3. Let's try the same thing for This is the double angle formula for cosine but by substiuting some identities we can express it in a couple other ways.

  4. Double-angle Formula for Tangent

  5. Summary ofDouble-Angle Formulas

  6. We can also derive formulas for an angle divided by 2. Half-Angle Formulas As stated it is NOT both + and - but you must figure out where the terminal side of the angle is and put on the appropriate sign for that quadrant.

  7. We could find sin 15° using the half angle formula. Since 15° is half of 30° we could use this formula if  = 30° 30° 30° 15° is in first quadrant and sine is positive there so we want the +

  8. Let's draw a picture. 5 4   -3 Use triangle to find values.

  9. If  is in quadrant II thenhalf  would be in quadrant I where sine is positive 5 4   -3 Use triangle to find cosine value.

  10. Your Turn: Simplify an Expression • Simplify cot x cos x + sin x. • Click for answer.

  11. Your Turn: Cosine Sum and Difference Identities • Find the exact value of cos 75°. • Click for answer.

  12. Your Turn: Sine Sum and Difference Identities • Find the exact value of . • Click for answer.

  13. Your Turn: Double-Angle Identities • If , find sin 2x given sin x < 0. • Click for answer.

  14. Your Turn: Double-Angle Identities

  15. Your Turn: Half-Angle Identities • Use a half-angle identity to find sin 22.5°. • Click for answer.

  16. Verifying An Identity Using Double Angle Objective: 7-4 Double-Angle and Half-Angle Identities

  17. Find using the double angle formulas. (no calculator) 1. sin 420° 2. 3. tan 240° 4. 5. cos 300° 6. tan 630°

  18. Find the exact values of sin 2x, cos 2x, and tan 2x using the double angles formulas 1. 2.

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