What values for theta(0 less than or equal to theta less than or equal to 2pi) satisfy the equation? 2 sin theta cos theta+ (Sqrt of 2)cos theta=0

Question

What values for theta(0 less than or equal to theta less than or equal to 2pi) satisfy the equation?
2 sin theta cos theta+ (Sqrt of 2)cos theta=0

Answer 1

2sinθcosθ + √2cosθ = 0 , 0 ≤ θ ≤ 2π

 

cosθ(2sinθ + √2) = 0

 

So, cosθ = 0 or sinθ = -√2/2

 

If cosθ = 0, then θ = π/2, 3π/2

 

If sinθ = -√2/2, then θ = 5π/4, 7π/4

 

 

 

Answer 2

Let x = theta

 

2sin(x)cos(x) + cos(x)√2 = 0

 

 

Factor out cos(x).

 

cos(x)(2sin(x) + √2) = 0

 

 

Set cos(x) equal to zero.

 

cos(x) = 0

 

x = π/2

x = 3π/2

 

The solutions are

 

x = π/2             and            x = 3π/2