Solve for theta in the interval 180 to 270

Question

sin theta + radical 2= -sin theta

Answer 1

I think you mean the following:

 

sin (θ) + √2 = -sin (θ)

 

Add sin (θ) to both sides:

2 sin (θ) + √2 = 0

 

Subtract √2 from both sides:

2 sin (θ) = -√2

 

Divide both sides by 2:

sin (θ) = -√2/2

 

The interval from 180° to 270° is the third quadrant.  The sine function is negative in the third quadrant, so that's good  that we are looking for an angle with a negative sine.

 

Remember that sin 45° is √2/2.  To find the third quadrant angle that corresponds to 45°, add 180°.  That gives you 225°.