Sin, Cos, Tan and the Unit Circle

With sin30˚ = 1/2, cos45˚ = √2/3, and tan60˚ = √3, how do these results relate to the unit circle and how can we use these results to find the sine, cosine and tangent of other angles?

Firstly, what is a unit circle? A unit circle is simply a circle, centred about the origin (0,0), with a radius of 1 unit.

Sine, cosine and tangent, as well as being called trigonometric functions, are also called circular functions. This is because every point on a unit circle can be described in terms of these functions.

In this video, I show you how the x and y-coordinates of a point on the unit circle cosine and sine of the angle of the point with respect to the horizontal.

Using this principle, we then find the sine and cosine of angles that are larger than 90˚ (i.e. obtuse and reflex angles).

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