Question

the point (-3,2) is on the terminal side of an angle t. find sin(t) to 2 decimal places.

Answer 1

Hi there. Are you interested in learning how to solve the problem or really just here for the answer?

Answer 2

i am interested in learning how to solve the equation. i believe I use r=sq root of x^2+y^2 right?

Answer 3

yep, exactly!

Answer 4

You can think of sin(t) being the Y coordinate if the circle were of a standard radius of 1. So the easiest way to solve the problem is just "scale down" the y coordinate by dividing it by the length of that ray, which as you pointed out is sqrt(x^2 + y^2)

Answer 5

ok. now I come up with sq rt of 13 for r. how do i proceed?

Answer 6

If you have a circle with r=1, then the angle to any point on that circle has a sin value of the point's y coordinate.

Answer 7

you have a larger circle - one that goes through (-3, 2) - so you can find the sin value of points on that circle by dividing the y coordinate by the length. So just divide the y coordinate by the length you computed.

Answer 8

so sin(t)=y/r and my problem would be -2/13 ? or -0.55 ? will my answer be negative?

Answer 9

I think you got the negative sign mixed up - your point is (-3, 2), right?

Answer 10

yes. you are right. thank you. i was looking at another similar problem. thank you!

Answer 11

thank you for learning rather than just asking for the answer!