Section 5.3 handout ann

Section 5.3 handout ann - Use the Power Reducing Formulas...

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Section 5.3 Double Angle and Half Angle Formulas, Page 1 Section 5.3: Double Angle & Half Angle Formulas 1) Objective 1: Use the Double Angle Formulas . a. Double Angle Formulas sin 2 θ = 2sin θ cos θ c os 2 θ = cos 2 θ – sin 2 θ = 2cos 2 θ – 1 = 1 – 2sin 2 θ t an 2 θ = θ θ 2 tan 1 tan 2 - b. See Problem #10, page 573 2 nd ed or page 597 3 rd ed. Find sin2 θ , cos2 θ , and tan 2 θ if cos θ = 40/41 and θ is in Quadrant IV. Section 5.3 Double Angle and Half Angle Formulas, Page 1 θ
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Section 5.3 Double Angle and Half Angle Formulas, Page 2 c. See Problem #16, page 573 2 nd ed or page 597 3 rd ed. Find the exact value of the expression 2sin 22.5 o cos 22.5 o . How does this relate to the formulas above? Look at sin2 θ = 2sin θ cos θ . Section 5.3 Double Angle and Half Angle Formulas, Page 2
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Section 5.3 Double Angle and Half Angle Formulas, Page 3 2) Objective 2:
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Unformatted text preview: Use the Power Reducing Formulas . You will find these useful in Calculus with Analytic Geometry. a. Power Reducing Formulas sin 2 θ = 2 2 cos 1 θ-cos 2 θ = 2 2 cos 1 θ + tan 2 θ = θ θ 2 cos 1 2 cos 1 +-b. Change sin 4 θ to something with exponents of 1. 3) Objective 3: Use the Half Angle Formulas . a. Half Angle Formulas 2 cos 1 2 sin θ θ-± = 2 cos 1 2 cos θ θ + ± = θ θ θ cos 1 cos 1 2 tan +-± = = θ θ sin cos 1-= θ θ cos 1 sin + You need to know what quadrant θ /2 is in to assign the + or – to the square root. b. Find sin 22.5 o Section 5.3 Double Angle and Half Angle Formulas, Page 3 Section 5.3 Double Angle and Half Angle Formulas, Page 4 Section 5.3 Double Angle and Half Angle Formulas, Page 4...
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