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Finding Exact Values of Trig Ratios

Finding Exact Values of Trig Ratios. Special Right Triangles. 30-60-90. Special Right Triangles. 45-45-90. Consider the Special Angles in relation to the Unit Circle….

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Finding Exact Values of Trig Ratios

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  1. Finding Exact Values of Trig Ratios

  2. Special Right Triangles • 30-60-90

  3. Special Right Triangles • 45-45-90

  4. Consider the Special Angles in relation to the Unit Circle… • Since the radius is always 1 and we know that the sine, cosine, and tangent values are always determined by the point through which the terminal ray passes, we can construct the following….

  5. 30 Degree Angle

  6. 60 Degree Angle

  7. 45 Degree Angle

  8. Values to Memorize

  9. Reference Angles • We have previously learned that if the angle is the same size, then it will have the same values (but the + or – may switch depending upon the quadrant) • A Reference Angle is the acute angle formed by the terminal ray and the x-axis • The Reference Angle tells us the size of the triangle

  10. Examples • Give the reference angle for each of the following angles:

  11. Examples • Give the reference angle for each of the following angles:

  12. Examples • Give the reference angle for each of the following angles:

  13. Examples • Give the reference angle for each of the following angles:

  14. Reference Angles (in Radians) • What can we observe about the reference angle in each radian measure?

  15. Exact Values of Special Angles • Find the exact value for each of the following:

  16. Exact Values of Special Angles • Find the exact value for each of the following:

  17. Exact Values of Special Angles • Find the exact value for each of the following:

  18. Exact Values of Special Angles • Find the exact value for each of the following:

  19. Exact Values of Special Angles • Find the exact value for each of the following:

  20. Exact Values of Special Angles • Find the exact value for each of the following:

  21. Homework • Pg. 280 (1-4, 11-18)

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