Question 525104: My question is:
Suppose that you did not have a unit circle on the circle, but instead a circle with the radius of 5. Will the angle measure in degrees and/or radians change? Why or why not?
Please help. I think that it does NOT change but I'm not absolutely sure and I do not know how to explain it.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! My question is:
Suppose that you did not have a unit circle on the circle, but instead a circle with the radius of 5. Will the angle measure in degrees and/or radians change? Why or why not?
Please help. I think that it does NOT change but I'm not absolutely sure and I do not know how to explain it.
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Let's say we are working with a reference angle in quadrant I of a unit circle, sin and cos are the y and x-coordinates of the circle. Sin=y/radius or the hypotenuse, but in a unit circle, we know the value of y and x are the values of sin and cos at a given angle without thinking what the hypotenuse might be because it is equal to 1. But we must always remember that sin and cos and all the other trig functions are ratios, not a fixed number.
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Now, to your point about working with a circle with a radius other than 1, like 5, as you mentioned. If you took a unit circle and increased its radius, the sin and cos values will no longer be the y and x coordinates of the circle but would be the ratio of y/radius and x/radius. This would apply to any circle with different radii. It is important to remember that you are still working with a right triangle that is proportional to the unit circle right triangle and all the trig fundamentals based on the unit circle still apply. To answer your question, the angle measure doesn't change regardless of the value of the radius. On revolution of a circle will always be 2π radians or 360º, and the quadrant in which the terminal side is determines the sign of the trig function. Bottom line, procedures for angle measurements are not affected by changes in radius. Hope this helps.
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