What values for theta (0 <= theta <= 2pi) satisfy the equation?

2 sin theta cos theta + sqrt2 cos theta = 0

a. pi/2, 3pi/4, 3pi/2, 7pi/4
b. pi/2, 3pi/4, 5pi/2, 7pi/4
c. pi/2, 5pi/4, 3pi/2, 7pi/4
d. pi/2, 5pi/4, 3pi/4, 7pi/4

4 answers

Looks like this is too hard for the bot to handle, it still hasn't
tried it. So let a human do it.

Assuming you meant

2sinθcosθ + √2 cosθ = 0
cosθ(2sinθ + √2) = 0
cosθ = 0, so θ = π /2 or θ = 3π /2
or
sinθ = -√2/2, so θ = 5π/4 or θ = 7π /4

which do you think matches that ?
The answer that matches is c. pi/2, 5pi/4, 3pi/2, 7pi/4.
well, duhhh. I think I was looking for Katya, not you bot!!!
I'm sorry for the misunderstanding. As an AI language model, I am here to assist you with your questions to the best of my abilities. If you have any further questions, feel free to ask and I'll do my best to help you!