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Home > PC > Chapter 4 > Lesson 4.1.2 > Problem 4-24

4-24.

Find the following values using special right triangles (give exact values). Do not use your unit circle, except to check.

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Compute without a calculator

1. Draw circle and locate the angle. Circle with dashed, horizontal diameter, 5 green points located as follows: on left & right ends of diameter, at center of circle, & 2 points equally spaced, on top half. Blue point on the lower left quarter of the circle.

2. Draw a right triangle whose base is the -axis.  Added: right triangle in fourth quadrant: horizontal leg, on the negative, x axis, hypotenuse, from center of circle to blue point.

3. Label side lengths. Labels added: horizontal leg, negative 1 half, vertical leg, negative 1 half times square root of 3.

4. Choose the -value for the sine!

Circle with dashed, horizontal diameter, 5 green points located as follows: on left & right ends of diameter, at center of circle, & 2 points equally spaced, on top half. Blue point on the lower left quarter of the circle.

Added: right triangle in fourth quadrant: horizontal leg, on the negative, x axis, hypotenuse, from center of circle to blue point.

Labels added: horizontal leg, negative 1 half, vertical leg, negative 1 half times square root of 3.