If the point P(-4/5,y) lies on the unit circle and P is in the third quadrant, what does y equal? If necessary, use the slash mark ( / ) for a fraction bar.

Question

anonymous · Answer

$$-\frac{3}{5}$$

jim_thompson5910 · Answer

Use the fact that $$x^2+y^2=1$$ is the equation of the unit circle.

We know that x=-4/5, so plug this in and solve for y

$$x^2+y^2=1$$ 

$$(-\frac{4}{5})^2+y^2=1$$ 


$$\frac{16}{25}+y^2=1$$ 


$$y^2=1-\frac{16}{25}$$ 


$$y^2=\frac{9}{25}$$ 


$$y=-\sqrt{\frac{9}{25}}$$ 


Note: we're in the 3rd quadrant, so y is negative. So we use the negative square root.


$$y=-\frac{3}{5}$$

anonymous · Answer

thank you

anonymous · Answer

jimthompson is correct and so is the method. however, every math teachers favorite right triangle is 3 - 4 - 5.  this is a 3, 4 5  right triangle which is why you can do it in your head after you have seen a few

anonymous · Answer

if you divide 3, 4, 5 by 5 you get 
$$\frac{3}{5},\frac{4}{5},1$$ so it is the same triangle just scaled so that the hypotenuse is 1

anonymous · Answer

you will see this often along with 5, 12, 13 scaled as 
$$\frac{5}{13},\frac{12}{13},1$$