20. DOUBLE-ANGLE and HALF ANGLE IDENTITIES

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Presentation transcript:

20. DOUBLE-ANGLE and HALF ANGLE IDENTITIES

Double Angle Formulas Half Angle Formulas The + or – depends in which quadrant the original given value exists

Two types of double angle problems 1. verify/simplify 2. given a trig value find values of double angles

Type 1

Simplify

Simplify

Simplify

Simplify

Verify the identity

Verify the identity

Prove

Type 2

Let's draw a picture. 5 4   -3

Let's draw a picture.  1  4

Half Angle

Ex: Use the half angle formula to find the exact value of sin(105o) 105 exists in the II, so sine is positive! 2. Double 105 to get the numerator 3. Plug into the half formula 4. 5. Simplify

Find the exact value of the function.