How to calculate points on the unit circle for specific angles

To calculate points on the unit circle for a specific angle $ \theta $, follow these steps:

1. Recall that the unit circle is a circle with radius 1 centered at the origin (0,0).

2. Points on the unit circle are given by the coordinates $( \cos(\theta), \sin(\theta) )$, where $ \theta $ is the angle in radians measured from the positive x-axis.

3. For example, for $ \theta = \frac{ \pi }{4} $, the coordinates are:

$ ( \cos( \frac{ \pi }{4} ), \sin( \frac{ \pi }{4} ) ) = ( \frac{ \sqrt{2} }{2}, \frac{ \sqrt{2} }{2} ) $

To calculate points on the unit circle for a specific angle $ heta $:

1. The unit circle has a radius of 1.

2. Use the coordinates $( cos( heta), sin( heta) )$.

3. For $ heta = frac{ pi }{6} $, the coordinates are:

$ ( cos( frac{ pi }{6} ), sin( frac{ pi }{6} ) ) = ( frac{ sqrt{3} }{2}, frac{ 1 }{2} ) $

To calculate points on the unit circle:

1. Use the formula $( cos( heta), sin( heta) )$.

2. For $ heta = frac{ pi }{3} $:

$ ( cos( frac{ pi }{3} ), sin( frac{ pi }{3} ) ) = ( frac{ 1 }{2}, frac{ sqrt{3} }{2} ) $

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