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Home > PC > Chapter 4 > Lesson 4.1.2 > Problem 4-29


Circle centered at the origin, labeled, O, diameter from point in second quadrant labeled, B, to point in fourth quadrant labeled, I, & diameter from point in third quadrant labeled, T, to point in first quarant labeled, W, segments connecting, B to T, & from, W to I, intersecting x axis at point labeled, E, curved arrow from positive x axis to radius in first quadrant labeled alpha, curved arrow from positive x axis to radius in second quarant labeled, beta.  You can use the image of a BOW TIE to remind you to always draw a vertical line to the -axis when completing a triangle to compute sine and cosine. This is because the triangle you work with will always be part of the bow tie.

In the diagram, assume the bow tie is symmetric with respect to both coordinate axes. Let EOW, EOB, EOT, and EOI, where all of these angles are in standard position and between and . The angles for and are shown. Assume sin .

  1. Without finding , find the exact values for , , and .

  2. Use the Fundamental Pythagorean Identity or a right triangle to find .

  3. Find the exact values for , , and .

The first two are negative .

The last one is positive .