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October 24, 2012 Unit Circle Warm-up! Your right arm is the initial side and your left arm is the terminal side. Ready? Let’s go! 43 22 4 7 6 6 -270° 3 Lesson 4.3 Special Triangles 45-45-90 and 30-60-90 The ratio of the 45-45-90 triangle is: 1: 1: √2 The ratio of the 30-60-90 triangle is: 1: √3: 2 Make a table of the 6 trig functions for the special triangles. Θ = 30° or π/6 Θ = 45° or π/4 Θ = 60° or π/3 CW 4.3: Pg. 308 #17-26 Use the table we just completed to help you. What do the Unit Circle and Special Right Triangles have in common? • In groups of 2-3, follow the GeoSketchpad Instructions and answer the questions along the way on a separate sheet of paper. 60 30 45 45 Let’s go around the circle! 3rd and 4th quadrant Ms. PD! Show them how to use the reference angle! It makes the unit circle easier! Lesson 4.4 Use the reference angle to help you find all the points around the unit circle. A reference angle is the acute angle formed by the terminal side of θ and the x-axis. 75 For example, the reference angle of 225° is 45° . 64 6 4 6 5 6 Sketch the angle, then find the reference angles for the following: 1. 240° 4 2. 3 11 3. 6 How the reference angle works… • All you need to remember is the first quadrant and the reference angle. Putting it all together!!! • Each point on the unit circle corresponds to the cosine and sine of the angle. • The x-coordinate is the cosine. • The y-coordinate is the sine. • So each point on the unit circle is (cos , sin) Putting it all together in song!