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Understanding Coterminal Angles in Trigonometry

Learn how coterminal angles in trigonometry can have the same initial and terminal sides but different measures. Find coterminal angles, evaluate trig functions of nonquadrantal angles, use reference triangles, and explore trig ratios. Discover the unit circle and its significance in trigonometry.

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Understanding Coterminal Angles in Trigonometry

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  1. 4.3 Trigonometry Extended: The Circular Functions

  2. Initial Side, Terminal Side

  3. Positive Angle, Negative Angle

  4. Coterminal Angles Two angles in an extended angle-measurement system can have the same initial side and the same terminal side, yet have different measures. Such angles are called coterminal angles.

  5. Example Finding Coterminal Angles

  6. Example Finding Coterminal Angles

  7. Example Finding Coterminal Angles

  8. Example Finding Coterminal Angles

  9. Example Evaluating Trig Functions Determined by a Point in QI

  10. Example Evaluating Trig Functions Determined by a Point in QI

  11. Trigonometric Functions of any Angle

  12. Evaluating Trig Functions of a Nonquadrantal Angle θ • Draw the angle θ in standard position, being careful to place the terminal side in the correct quadrant. • Without declaring a scale on either axis, label a point P (other than the origin) on the terminal side of θ. • Draw a perpendicular segment from P to the x-axis, determining the reference triangle. If this triangle is one of the triangles whose ratios you know, label the sides accordingly. If it is not, then you will need to use your calculator.

  13. Evaluating Trig Functions of a Nonquadrantal Angle θ 4. Use the sides of the triangle to determine the coordinates of point P, making them positive or negative according to the signs of x and y in that particular quadrant. 5. Use the coordinates of point P and the definitions to determine the six trig functions.

  14. Example Evaluating More Trig Functions

  15. Example Evaluating More Trig Functions

  16. Example Using one Trig Ration to Find the Others

  17. Example Using one Trig Ration to Find the Others

  18. Example Using one Trig Ration to Find the Others

  19. Unit Circle The unit circle is a circle of radius 1 centered at the origin.

  20. Trigonometric Functions of Real Numbers

  21. Periodic Function

  22. The 16-Point Unit Circle

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