Trigonometry( studying trigonometry)

Question

Besides finding out the hypotenuse as we know as the radius. Is there another way to find out if the sine of any angle touches the circumference of the unit circle? Whether the coordinate is on the circumference of the unit circle.

For example: x=0.6 and y=0.8 and the radius=1

But if x=0.6 and y =0.79 the radius=0.99 so the coordinate:( 0.6, 0.79) doesn't touch the circumference of the unit circle

Answer 1

x^2 + y^2 = r^2 = 1^2 = 1

x^2 + y^2 = 1

.6^2 + .8^2 = .36+.64 = 1

whatever the point (x,y), plug it into x^2 + y^2 and if it doesn't sum to 1, it's not a point on the circle.

.6^2 + .79^2 = about .99< 1 so it's not on the circle

x^2 + y^2 = 1

x=rcos(theta) y = rsin(theta)

cos^2(theta) + sin^2(theta) = 1

r^2cos^2(theta) + r^2sin^2(theta) = r^2