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Home > PC3 > Chapter 4 > Lesson 4.2.1 > Problem 4-61

4-61.

Unit Circle, with a right triangle in third quadrant, using Point, w, on the circle, horizontal leg on negative, x axis, vertical leg, V W, is labeled 0.62. Central angle, from the positive, x axis, to the radius in third quadrant, labeled theta, with a curved arrow, pointing counter clockwise.Study the diagram of the unit circle at right.  

If is the origin, . Use the Pythagorean Theorem to determine .

This angle is in Quadrant III. Should and each be considered positive or negative?

  1. Evaluate .

  2. Evaluate .

  3. If α is another angle with the same sine as , but a different cosine, in what quadrant is ?

    For , sine and cosine are both negative.
    In what quadrant is sine negative and cosine positive?

  4. If  is another angle with the same cosine as , but a different sine, in what quadrant is ?

    For , sine and cosine are both negative.
    In what quadrant is sine positive and cosine negative?