Can Trigonometry Be Applied to Circles with a Radius Other Than 1?

[Lobdell]

I understand how trigonometry is related to the Unit Circle, but is there any way I can relate the same concept to circles with a radius other than 1?

Thanks in advance.

 

[Nimz]

Sure. You just need to insert a scaling factor. E.g., if you have a circle of radius 5 centered on the origin, (5 cos t, 5 sin t) will be a point on that circle. You can also move the circle away from the origin. If r = radius of the circle and (h, k) is the center of the circle, it shouldn't be too hard to figure out what the points on the circle are, using trig functions.

 

[HallsofIvy]

On the unit circle, cos(t) and sin(t) are defined, respectively, as the x and y coordinates of the point at distance t, measured along the circumference of the circle, from (1, 0). If the angle at (0,0) is measured in radians, then the angle is the same as t- that's essentially the definition of radian measure. If the circle has radius, r, other than 1, then the angle is the distance along the circle, divided by r.