How does the unit circle connect the right triangle definitions of sine, cosine, and tangent to coordinate...
Why does the equation x^2 + y^2 = 1 make sense for every point on the unit circle?
The unit circle connects the right triangle definitions of sine, cosine, and tangent to coordinate points by using the coordinates of a point (x, y) on the circle. The x-coordinate gives the cosine value, and the y-coordinate gives the sine value. Tangent is the ratio of sine to cosine, or y/x, as long as x ≠ 0. This allows the trigonometric functions to be expressed in terms of the coordinates of points on the unit circle.
The equation x^2 + y^2 = 1 makes sense for every point on the unit circle because the unit circle is defined as having a radius of 1. According to the Pythagorean Theorem, for any point (x, y) on the circle, the sum of the squares of the x and y coordinates must equal the square of the radius, which is 1. Therefore, x^2 + y^2 = 1 for all points on the unit circle.
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