unit circle: if tanθ = -2/3 and θ is in quadrant II, what is the value of cosθ ?

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Alpha6

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I am ripping out my hair here, I can't get this.

The problem is if tanθ = -2/3 and θ is in quadrant II, what is the value of cosθ ?

so I figured if tan of θ is opposite over adjacent, cosθ = adjacent over hypotenuse.

So I took the adjacent (-)3 over sqrt(13.

I got an answer of -.82305

but the calculator says that sin of 2/3 is .61837.


What am I doing wrong?
 
Alpha6 said:
I am ripping out my hair here, I can't get this.

The problem is if tanθ = -2/3 and θ is in quadrant II, what is the value of cosθ ?

so I figured if tan of θ is opposite over adjacent, cosθ = adjacent over hypotenuse.

So I took the adjacent (-)3 over sqrt(13.
Click to expand...
Done! You want the cosine, not the sine or the angle. You simply went too far.

-Dan
 
Yes.

To check, my calculator shows that [MATH]\cos(\tan^{-1}(-2/3)) = 0.83205[/MATH].
 
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