Trigonometry
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Trigonometry

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 Trigonometric Equations: Solve the equation, 2sin²θ - sinθ = 0                           This is a Quadratic Equation as in 2x² - x = 0                                          By factorization, Sinθ(2sinθ - 1) = 0                                                 So, sinθ = 0 and 2sinθ - 1 = 0                                                  When sinθ = 0, angle θ = 0º, 180º and 360º                                                        Also, for 2sinθ - 1 = 0                                                              sinθ = 0.5. Angle θ = 30º and 150º                Answer: Solutions of θ are 0º, 30º, 150º, 180º and 360º Polar Equations: Find the Polar Equation of the Circle whose Cartesian Equation is x² + y² = 4x.              If x = rcosθ and y = rsinθ         then r²cos²θ + r²sin²θ = 4rcosθ                 r²(cos²θ + sin²θ) = 4rcosθ                       Therefore, r² = 4rcosθ                                        r = 4cosθ                   Polar Equation is r = 4cosθ

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