Question

If tan theta=0.4,when theta lies between 0°and360°,write down the possible values of theta and sin theta

Answer 1

Answer:

θ = 21.8°   & 201.8°

Sinθ = ± 0.371

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°