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Understanding Special Angles: Trigonometric Values for 30° and 60° in Equilateral Triangles

Master the special angles of 30° and 60° through the properties of equilateral triangles. Learn how to drop a perpendicular bisector to create a 30-60-90 triangle. Memorize key trigonometric values using the SOH-CAH-TOA method for both angles. This guide also covers reference angles and the trigonometric values for 120°, exploring how these relate to the quadrants. Perfect your understanding and application of trigonometric functions to succeed in your math studies. Homework exercises are provided to reinforce these concepts.

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Understanding Special Angles: Trigonometric Values for 30° and 60° in Equilateral Triangles

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  1. 7.3 Special Angles(30 & 60)

  2. Equilateral Triangle 60 angles w/ sides = 1 Drop Perpendicular Bisector to form 30-60-90  60 30 1 1 60 60 60 1 30

  3. Memorize!! Trig Values for 30 SOH – CAH – TOA 60 Hyp Opp 30 Adj = 2 reciprocals

  4. Memorize!! Trig Values for 60 SOH – CAH – TOA 60 Hyp Adj 30 Opp reciprocals = 2

  5. Related (Reference) Angles Positive acute  that terminal side makes w/ x-axis y Reference  for 120 is 60 Have SAME trig values, except possibly sign Sign depends on Quadrant the  is in 120 60 x

  6. Find the exact values of the trig functions of 120 y 120 Reference  for 120 is 60 Trig Values same as 60 except signs 120 is in QII, x is (–), y is (+) 60 x

  7. Homework #706 Pg. 407 59, 61 – 63, 66 & Do angles & Memorize 30 & 60 Trig Values

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