solve problem

Question

GIVEN THAT SINθ=0.3657 AND θ IS IN QUADRANT I, FIND SIN 2θ

 

SIN 2θ=

Answer 1

First, we need to know the double angle identity for sine.

 

sin2θ = 2sinθcosθ

 

sinθ is already given to us.  We just need to find cosθ.

 

 

We know that   sin²θ + cos²θ = 1

 

 

cosθ = √(1 - sin²θ)

 

 

Therefore,

 

sin2θ = 2sinθ√(1 - sin²θ)

 

Plug in the value of sinθ into the identity and simplify.