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If tan theta = 0.4 when theta lies between 0 and 360° |
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Answer» Answer: θ = 21.8° & 201.8° Step-by-step explanation: If tan theta=0.4,when theta lies between 0°and360°,write down the POSSIBLE values of theta and SIN theta Tanθ = Sinθ / Cosθ Cos²θ + Sin²θ = 1 => Cosθ = √(1 - Sin²θ) = Tanθ = Sinθ / √(1 - Sin²θ) = 0.4 = Sinθ / √(1 - Sin²θ) = Sinθ = 0.4 * √(1 - Sin²θ) Squaring both sides Sin²θ = 0.16 * (1 - Sin²θ) = 1.16Sin²θ = 0.16 = Sin²θ = 0.16/1.16 = Sin²θ = 0.138 = Sinθ = ± 0.371 As tanθ is +ve so if Sinθ is + ve then Cosθ should be +ve & when Sinθ is -ve then cosθ should be - ve => θ lies in 1st quadrant & 3rd Quadrant θ = 21.8° & 201.8° |
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