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5.1 The Unit Circle

5.1 The Unit Circle. Unit circle – the circle with radius 1 centered at the origin in the xy -plane. The equation is: x 2 + y 2 = 1. EX. Recall: Show that (1, -3) is on the line 2x + 3y = -7 EX. Ex. Terminal Points.

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5.1 The Unit Circle

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  1. 5.1 The Unit Circle

  2. Unit circle – the circle with radius 1 centered at the origin in the xy-plane. The equation is: x2 + y2 = 1

  3. EX • Recall: Show that (1, -3) is on the line 2x + 3y = -7 EX

  4. Ex

  5. Terminal Points • Start at (1, 0) and move ccw if t is positive and cw if t is negative. • We arrive at the point P(x, y) on the unit circle. P(x, y) is the terminal point determined by the real number t.

  6. The circumference of the unit circle is C = 2 If a point starts at (1, 0) and moves ccw all the way around and returns to (1, 0), then we have traveled a distance of 2 pi . • Travel half way around = _________ • Travel a quarter of the way around = ______

  7. ExFind the terminal point on the unit circle determined by each real number t. • Different values of t can determine the same terminal point.

  8. The unit circle is symmetric with respect to the line y = x. Then you can solve a system of equations to find the terminal points. OR you can memorize the table below:

  9. The Reference Number • Let t be a real number.

  10. EXFind the reference number

  11. ExFind the terminal points determined by each given real number t.

  12. Since the circumference is 2 pi, the terminal point determined by t is the same as that determined by t + 2pi or t – 2pi. • In general, we can add or subtract 2pi any number of times without changing the terminal point determined by t.

  13. EXFind the terminal point

  14. ExFind the terminal points

  15. Ex

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