# Thread: finding an angle in a circle given a point of (0.6, Y)

1. ## finding an angle in a circle given a point of (0.6, Y)

Basic a unit circles is given
______
| / (0.6,Y)
| /
| /
|A)________

Find angle A and Y, two decimal place

So far I got this

Since point is =(cosA,sinA), Y must equal to (Sin angle A)
Then how would you find angle A. No radius or arc length is given! please help.

2. Originally Posted by jepal
Basic a unit circles is given
______
| / (0.6,Y)
| /
| /
|A)________

Find angle A and Y, two decimal place

So far I got this

Since point is =(cosA,sinA), Y must equal to (Sin angle A)
Then how would you find angle A. No radius or arc length is given! please help.
Hi jepal,

$\displaystyle \cos A =.6$

This means that $\displaystyle \cos A=\frac{x}{r}=\frac{6}{10}=\frac{3}{5}$

$\displaystyle x=3$
$\displaystyle r=5$

Use the Pythagorean Theorem to find y.

$\displaystyle r^2=x^2+y^2$

$\displaystyle 5^2=3^2+y^2$

$\displaystyle y=4$

So $\displaystyle \sin A = \frac{y}{r}=\frac{4}{5}=.8$

Your point is $\displaystyle (.6, .8)$

Your angle is $\displaystyle \cos^{-1}\frac{3}{5} \ \ or \ \ \sin^{-1}\frac{4}{5}$ or approximately $\displaystyle 53.1^{\circ}$

3. Originally Posted by masters
Hi jepal,

$\displaystyle \cos A =.6$

This means that $\displaystyle \cos A=\frac{x}{r}=\frac{6}{10}=\frac{3}{5}$

$\displaystyle x=3$
$\displaystyle r=5$

Use the Pythagorean Theorem to find y.

$\displaystyle r^2=x^2+y^2$

$\displaystyle 5^2=3^2+y^2$

$\displaystyle y=4$

So $\displaystyle \sin A = \frac{y}{r}=\frac{4}{5}=.8$

Your point is $\displaystyle (.6, .8)$

Your angle is $\displaystyle \cos^{-1}\frac{3}{5} \ \ or \ \ \sin^{-1}\frac{4}{5}$ or approximately $\displaystyle 53.1^{\circ}$
Thank you, but how did u get 10, is it an assumption that radius is 10?

4. Originally Posted by jepal
Thank you, but did I just assume radius is 10, when no radius is given!
What is the fractional form of the decimal number "0.6"?

5. i figured that was the answer, but what is r then? im so confused! wouldnt it be

cos A=x/r

cos A=06./r? no? Please explain. Thanks