Unformatted text preview: in QI and its re±ection − 3 θ =− π 3 around the xaxis in QIV. Adding multiples of 2 π to these gives us: 3 θ = ± π 3 + 2 π k for k = 0, ± 1, ± 2, . .. So dividing everything by 3 we get the general solution for θ : θ = ± π 9 + 2 π 3 k for k = 0, ± 1, ± 2, . .. Example 6.7 Solve the equation sin 2 θ = sin θ . Solution: Here we use the doubleangle formula for sine: sin 2 θ = sin θ 2 sin θ cos θ = sin θ sin θ (2 cos θ − 1) = ⇒ sin θ = or cos θ = 1 2 ⇒ θ = 0 , π or θ = ± π 3 ⇒ θ = π k and ± π 3 + 2 π k for k = 0, ± 1, ± 2, . .....
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 Fall '11
 Dr.Cheun
 Calculus, Trigonometry, Equations, Sin, Expression, θ

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