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DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

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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

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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.

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Double-angle Formula for Tangent

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Summary of Double-Angle Formulas

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Page 262 #7 (a and b)

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Half-Angle Formulas We can also derive formulas for an angle divided by 2. 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.

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Page 262 #7 (a and b)

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

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Pages 262-263 (8, 12, 16, 20, 22, 24, 36, 48)

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Double Angle Formulas T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use those formulas.

Double Angle Formulas T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use those formulas.

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