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- Amenah8

FIND FAETA: cos faeta = (-15/17), sin faeta > 0

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- Amenah8

FIND FAETA: cos faeta = (-15/17), sin faeta > 0

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- Michele_Laino

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

- Amenah8

Right, sorry!

- 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

|dw:1439224370587:dw|

- Amenah8

how did you know it was the 2nd quadrant?

- 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

since*

- Amenah8

oh, i get it!

- 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

and i would use the graphing circle

- Michele_Laino

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

- 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

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

- Amenah8

what do you mean by a data of my problem?

- Michele_Laino

|dw:1439224865101:dw|

- 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

belong*

- Amenah8

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

- Michele_Laino

yes!

- 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

but -\[-\sqrt{3}/2\] is close

- Michele_Laino

you have to find \theta, right?

- Michele_Laino

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

- Amenah8

how did you get 151.93?

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