## Amenah8 one year ago FIND FAETA: cos faeta = (-15/17), sin faeta > 0

1. Michele_Laino

do you mean cos(\theta) and sin(\theta), right?

2. Amenah8

Right, sorry!

3. Michele_Laino

the requested angle \theta lies in the second quadrant, since we have this drawing: |dw:1439224267236:dw|

4. Michele_Laino

|dw:1439224370587:dw|

5. Amenah8

how did you know it was the 2nd quadrant?

6. Michele_Laino

sionce if the point P, namely the second ends of your arc, lies in the second quadrant, then its x-coordinate, which is equal to cos(\theta) is negative, whereas its y-coordinate, which is sin(\theta) is positive, as requested from your problem

7. Michele_Laino

since*

8. Amenah8

oh, i get it!

9. Michele_Laino

so you have to find an angle whose measure is greater than 90 degrees and less than 180 degrees, whose cosine function is equal to -15/17

10. Amenah8

and i would use the graphing circle

11. Michele_Laino

for computation, you can use, for example, windows calculator

12. Amenah8

but if cos is just x, x=-15/7. so then how do we know y (sin) is positive? couldn't it have been in the 3rd quadrant?

13. Michele_Laino

sin(\theta) has to be positive, since it is a data of your problem

14. Amenah8

what do you mean by a data of my problem?

15. Michele_Laino

|dw:1439224865101:dw|

16. Michele_Laino

as we can see from my last drawing, only points which belongs to the first quadrant and second quadrant, have y-coordinate >0

17. Michele_Laino

belong*

18. Amenah8

oh, because in third and 4th quadrants, y is negative!

19. Michele_Laino

yes!

20. Amenah8

so how would i solve for theta? on the unit circle, the only x "coordinates" are the negative square root of 3 divided by 2, -1/2, and the negative square root of 2 divided by 2. None of those exactly equal -15/17.

21. Amenah8

but -$-\sqrt{3}/2$ is close

22. Michele_Laino

you have to find \theta, right?

23. Michele_Laino

if cos(\theta)= -15/17, then using windows calculator I got: \theta= 151.93 degrees, namely \theta= 152 degrees

24. Amenah8

how did you get 151.93?