If tan theta = 0.4 when theta lies between 0 and 360°
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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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