Amenah8
  • Amenah8
FIND FAETA: cos faeta = (-15/17), sin faeta > 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Michele_Laino
  • Michele_Laino
do you mean cos(\theta) and sin(\theta), right?
Amenah8
  • Amenah8
Right, sorry!
Michele_Laino
  • Michele_Laino
the requested angle \theta lies in the second quadrant, since we have this drawing: |dw:1439224267236:dw|

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Michele_Laino
  • Michele_Laino
|dw:1439224370587:dw|
Amenah8
  • Amenah8
how did you know it was the 2nd quadrant?
Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
since*
Amenah8
  • Amenah8
oh, i get it!
Michele_Laino
  • 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
Amenah8
  • Amenah8
and i would use the graphing circle
Michele_Laino
  • Michele_Laino
for computation, you can use, for example, windows calculator
Amenah8
  • 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?
Michele_Laino
  • Michele_Laino
sin(\theta) has to be positive, since it is a data of your problem
Amenah8
  • Amenah8
what do you mean by a data of my problem?
Michele_Laino
  • Michele_Laino
|dw:1439224865101:dw|
Michele_Laino
  • 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
Michele_Laino
  • Michele_Laino
belong*
Amenah8
  • Amenah8
oh, because in third and 4th quadrants, y is negative!
Michele_Laino
  • Michele_Laino
yes!
Amenah8
  • 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.
Amenah8
  • Amenah8
but -\[-\sqrt{3}/2\] is close
Michele_Laino
  • Michele_Laino
you have to find \theta, right?
Michele_Laino
  • Michele_Laino
if cos(\theta)= -15/17, then using windows calculator I got: \theta= 151.93 degrees, namely \theta= 152 degrees
Amenah8
  • Amenah8
how did you get 151.93?

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