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Type: Multiple-Choice
Category: Trigonometry
Level: Grade 11
Standards: HSF-TF.A.4
Author: nsharp1
Created: 4 years ago

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Trigonometry Question

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Let circle A be the unit circle centered at the origin. Assume that x1,x2,x3,x4,y1,y2,y3,y4 are all real numbers that are greater than or equal to zero.

Grade 11 Trigonometry CCSS: HSF-TF.A.4

For this investigation of trigonometric functions and their symmetry, the unit circle was used (circle A). Why was the unit circle used, and not a circle with a different radius (not equal to one unit)?
  1. Because the absolute value of the maximum and minimum values of the sine and cosine functions are 1.
  2. The circumference of a circle is C=2πr. If the radius is not equal to 1, the circumference would be greater than or less than 2π. Since the period of sine and cosine is 2π, this would mean that the values of these functions on the circle would not fit.
  3. It simplifies the math, allowing the coordinates of the points on the unit circle to be equal to the sine and cosine of angles in standard position.
  4. There is no particular reason, it is simply convention to use the unit circle. All the math and reasoning would have been exactly the same using a circle centered at the origin with a different radius.