## anonymous 3 years ago cos theta= - square root 2 divided by 2

1. Mertsj

$\cos \theta= -\frac{\sqrt{2}}{2}$

2. anonymous

yeah I need to solve the equation (0<theta<2pi)

3. Mertsj

We see that the cosine is negative. In what quadrants is the cosine negative?

4. anonymous

2 and 3

5. Mertsj

And on your unit circle, what angle has sqrt2/2 for its cosine?

6. anonymous

-45

7. Mertsj

45 does have that cosine ut we said we would be in quadrants II and III where the cosine is negative. Also you said your answer had to be between 0 and 2 pi so I think you should give the answer in radians.

8. Mertsj

How many radians is 45 degrees?

9. anonymous

45 degrees is pi/4

10. Mertsj

So...in quadrants II and III:

11. Mertsj

|dw:1368665856951:dw|

12. Mertsj

What is the angle meassured from the positive x axis?

13. anonymous

135

14. Mertsj

15. anonymous

3pi/4

16. Mertsj

Yes. And now for the third quadrant answer:

17. anonymous

5pi/4

18. Mertsj

|dw:1368666064142:dw|

19. Mertsj

Very good. And now you have your two answers. The angles between 0 and 2 pi that have a cosine of -sqrt2/2 are 3pi/4 and 5pi/4

20. anonymous

perfect