## UnbelievableDreams one year ago Confusing math question

1. UnbelievableDreams

Find all values of theta in the interval [0, 360] that have the given function valve. cos theta = -1/2

2. Astrophysics

Do you know your special triangles, 30-45-60

3. UnbelievableDreams

No, I think.

4. Astrophysics

|dw:1437017727352:dw|

5. Astrophysics

These are the special triangles, you should try to remember them, so we're given $\cos \theta = - \frac{ 1 }{ 2 } = \frac{ adj }{ hyp }$ so what is it

6. Astrophysics

Once we figure out the triangle, we can use the following information to find the quadrants it is in.

7. UnbelievableDreams

It is 60

8. Astrophysics

So for now, jut figure out $\cos \theta = \frac{ 1 }{ 2 }$

9. Astrophysics

Yeah :)

10. Astrophysics

Now we can figure out, where in the unit circle it would be negative, if you remember this thing called "CAST" |dw:1437018190660:dw| this shows where the trig ratios are positive

11. Astrophysics

So if you drew out triangles, you would notice for example in quadrant 4, y is negative but x is positive and also r (where x = adjacent, y = opposite, r = hypotenuse) and in quadrant 1 they are all positive, so quadrant 4 means costheta is positive, A means all positive, s means sin theta is positive, and t means tangent is positive.

12. Astrophysics

Sort of getting it?

13. Astrophysics

|dw:1437018375815:dw|

14. Astrophysics

So where in here would cos theta be negative?

15. UnbelievableDreams

IV?

16. UnbelievableDreams

@Astrophysics

17. Astrophysics

Well the quadrants here mean they are all positive in the certain area, so where it shows C that means it's positive, A means all of the ratios here are positive there, so for it to be negative it must be in Q2 and Q3 right?

18. UnbelievableDreams

Yes

19. Astrophysics

So for quadrant 2 we have $Q_2: 180 - 60 = ...$and for quadrant 3 we have $Q_3: 180 + 60 = ...$

20. UnbelievableDreams

120, 240

21. Astrophysics

Yup, those are your values then in the interval [0,360] :)