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DOUBLE-ANGLE AND HALF-ANGLE IDENTITIES. 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 x. Let's try the same thing for .

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## DOUBLE-ANGLE AND HALF-ANGLE IDENTITIES

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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 x**Let's try the same thing for**This is the double angle formula for cosine but by substituting some identities we can express it in a couple other ways.**Let's draw a picture.**5 4 x x’ -3 Use triangle to find values.**We can also derive formulas for an angle divided by 2**(called the half angle formula). We’ll do this by using the double angle formula for cosine that we found. Let’s solve this for sin Now let = x/2 In this formula 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.**We can also derive a half angle formula for cosine in a**similar manner. We’ll do this by using a different version of the double angle formula for cosine. Let’s solve this for cos Now let = x/2 In this formula 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.**Now to derive a half angle formula for tangent, let’s use**the fact that we know that tangent is sine over cosine and use their half angle formulas.**Summary**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.**We could find sin 15° using the half angle formula.**Since 15° is half of 30° we could use this formula if x = 30° 30° 30° 15° is in first quadrant and sine is positive there so we want the +**If is in quadrant II thenhalf would be in quadrant I**where sine is positive 5 4 x x’ -3 Use triangle to find cosine value.

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