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Home > A2C > Chapter 8 > Lesson 8.1.7 > Problem 8-104


What central angle, measured in degrees, corresponds to a distance around the unit circle of ?

What number of degrees is equivalent to  radians?

If you can't remember, calculate.

Now multiply the angle by .

  1. What other angles will take you to the same point on the circle?

    The distance around the unit circle is , no matter what point you start from.

  2. Make a sketch of the unit circle showing the resulting right triangle.

    The angle you are working with, , is more than . How much more?

    Unit Circle, with right triangle, hypotenuse from center, to a point, in first quadrant, on the circle, vertical leg, from point on circle, perpendicular to positive, x axis, horizontal leg, portion of positive, x axis. Counter clockwise curved arrow from hypotenuse, to positive, x axis, labeled, 7 pi thirds.

  3. Find , and exactly.

    Notice that the triangle formed is a triangle.