UnbelievableDreams
  • UnbelievableDreams
Confusing math question
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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UnbelievableDreams
  • UnbelievableDreams
Find all values of theta in the interval [0, 360] that have the given function valve. cos theta = -1/2
Astrophysics
  • Astrophysics
Do you know your special triangles, 30-45-60
UnbelievableDreams
  • UnbelievableDreams
No, I think.

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Astrophysics
  • Astrophysics
|dw:1437017727352:dw|
Astrophysics
  • 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
Astrophysics
  • Astrophysics
Once we figure out the triangle, we can use the following information to find the quadrants it is in.
UnbelievableDreams
  • UnbelievableDreams
It is 60
Astrophysics
  • Astrophysics
So for now, jut figure out \[\cos \theta = \frac{ 1 }{ 2 }\]
Astrophysics
  • Astrophysics
Yeah :)
Astrophysics
  • 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
Astrophysics
  • 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.
Astrophysics
  • Astrophysics
Sort of getting it?
Astrophysics
  • Astrophysics
|dw:1437018375815:dw|
Astrophysics
  • Astrophysics
So where in here would cos theta be negative?
UnbelievableDreams
  • UnbelievableDreams
IV?
UnbelievableDreams
  • UnbelievableDreams
@Astrophysics
Astrophysics
  • 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?
UnbelievableDreams
  • UnbelievableDreams
Yes
Astrophysics
  • Astrophysics
So for quadrant 2 we have \[Q_2: 180 - 60 = ...\]and for quadrant 3 we have \[Q_3: 180 + 60 = ...\]
UnbelievableDreams
  • UnbelievableDreams
120, 240
Astrophysics
  • Astrophysics
Yup, those are your values then in the interval [0,360] :)

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