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Trig Functions of Any Angle

Trig Functions of Any Angle. Lesson 2.3. θ. r. Angles Beyond 90 °. Expand from the context of angles of a right triangle Consider a ray from the origin through a given point (x, y). (x, y). •. β. Reference Triangle. Drop a perpendicular from (x,y) to the x-axis

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Trig Functions of Any Angle

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  1. Trig Functions of Any Angle Lesson 2.3

  2. θ r Angles Beyond 90° • Expand from the context of angles of a right triangle • Consider a ray from the origin through a given point (x, y) (x, y) •

  3. β Reference Triangle • Drop a perpendicular from (x,y) to the x-axis • This forms a reference triangle θ (x, y) Click to view spreadsheet example •

  4. Angles in Different Quadrants • Note that x and y have different signs in the various quadrants • Thus the trig functions will have different signs for the quadrants • For each quadrant, determine the signof the functions • I • II • IIIIV θ (x, y) •

  5. Angles in Different Quadrants • Remember "allsintancos" I II all positive sin is positive cos is positive tan is positive IV III

  6. Standard Angles • Recall table of functions of basic angles • Now we can expand this table

  7. 120° almost 90° 135° 150° 180° Standard Angles

  8. Assignment • Lesson 2.3 • Page 154 • Exercises 1 – 71 Odd

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