Explain how the special angles are used to find the coordinates points around the Unit Circle and how you find the sine, cosine, and tangent values of the special angles using the Unit Circle.

In the unit circle sine and cosine are given by the y-coordinate and x-coordinate, respectively. Tangent is the ratio y-coordinate / x-coordinate.

That is so in virtue of the unit circle has radius 1. That implies that the hypotenuse is 1, so sine is opposite-leg / hypotenuse = y-ccordinate / 1; and cosine is adjacent-leg / hypotenuse = x-coordinate / 1.

Some examples are:

1) Angle 0 ⇒ x-coordinate = 1, y-coordinate ⇒

cosine 0 = 1;

sine 0 = 0;

tangent = 0 / 1 = 0

2) Angle 45° ⇒ x-coordinate = (√2 ) / 2; y-coordinate = (√2) / 2 ⇒

cosine 45° = (√2 / 2)

sine 45° = (√2 ) / 2

tan 45° = 1

3) Angle 90° ⇒ x-coordinate = 0; y-coordinate = 1 ⇒

cos 90° = 0

sin 90° = 1

tan 90° = 1 / 0 = ∞ (undefined)

720

step-by-step explanation:

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