Question

Which of the following explains why Cosine 60 degrees = sine 30 degrees using the unit circle?

The answer is: The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.

But I would really appreciate someone to explain this to me, thank you!

Answer 1

Explanation:

Suppose triangle CAD with A = 60^0 and triangle ABE with B = 60^0. They are similar (the order matter, don't change the order)

We have CD = AE and AD = BE , AC = AB (radius)

in triangle CAD, cos A = cos (60) = AD/ AC

in triangle ABE, sin A = sin (30) = BE/AB

We have denominators are equal (both are radius of the circle) and numerator are equal, that gives cos (60) = sin (30)

Answer 2

The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.

Explanation:

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