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6.1.3 Unit Circle, Special Angles

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Building the “Unit Circle” For the unit circle, we will look into attempting to define and build the circle in terms of radians We can discover a pattern which will help you easily convert/memorize the patterns

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Special Triangles; 45-45-90 The special 45-45-90 triangle is one special triangle which will help us 1-1-√2 ratios What is 45 0 in radians? 90?

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Special Triangles; 30-60-90 The 30-60-90 will also help us Same type of relationship 1-2-√3 ratios What is 30 0 in radians? What is 60 0 in radians?

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Now, we can look at the unit circle as: – 1) A series of 45-45-90 triangles – 2) A series of 30-60-90 triangles We can split the unit circle into these 30-60-90 triangles and 45-45-90 triangles

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Positive/Negative Angle Measures On the unit circle, we can measure a positive or negative angle, depending on the direction of measurement Clockwise = Negative Angle Measure Counter-Clockwise = Positive Angle Measure

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Example. Find the indicated angle measure.

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The Whole Unit Circle

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Assignment Pg. 466 45-56 alls

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