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Section 4.3 The Unit Circle

Section 4.3 The Unit Circle. Quadrantal Angles. π 2. , 90˚. (0, 1). A. S. 0, 0˚ 2 π , 360˚. π , 180˚. (-1, 0). (1, 0). T. C. (0, -1). 3π 2. , 270˚. “ A ll S tudents T ake C alculus” tells you where each trig function is positive. Let’s begin with an easy family….

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Section 4.3 The Unit Circle

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  1. Section 4.3 The Unit Circle

  2. Quadrantal Angles π 2 , 90˚ (0, 1) A S 0, 0˚ 2π, 360˚ π, 180˚ (-1, 0) (1, 0) T C (0, -1) 3π 2 , 270˚ “All Students Take Calculus” tells you where each trig function is positive.

  3. Let’s begin with an easy family… What are the coordinates? Now, reflect the triangle to the second quadrant…

  4. What are the coordinates? Now, reflect the triangle to the third quadrant…

  5. What are the coordinates? Now, reflect the triangle to the fourth quadrant…

  6. What are the coordinates?

  7. **REMEMBER!!! cosθis represented by the x-coordinates and sin θis represented by the y-coordinates.** EX. Evaluate the six trig functions at θ = .

  8. EX. Evaluate the six trig functions at θ= . Homework: worksheet

  9. Complete the family… Now, reflect the triangle to the second quadrant.

  10. Now, reflect the triangle to the third quadrant.

  11. What are the coordinates? Now, reflect the triangle to the fourth quadrant.

  12. What are the coordinates?

  13. EX. Evaluate the six trig functions at θ = .

  14. EX. Evaluate the six trig functions at θ = . Homework: worksheet

  15. Complete the family… 60˚ Now, reflect the triangle to the second quadrant.

  16. What are the coordinates? Now, reflect the triangle to the third quadrant.

  17. What are the coordinates? Now, reflect the triangle to the fourth quadrant.

  18. What are the coordinates?

  19. Shortcut to remember ordered pairs in quadrant 1 • Parenthesis • Fractions with denominator of 2 • 3) • 4) Square roots 13 22 31

  20. EX. Evaluate the six trig functions at θ = .

  21. EX. Evaluate the six trig functions at θ = . Homework: worksheet

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