Question

Example 1: Choose a point in Quadrant 2, 3, or 4 to be on the terminal arm of an angle in standard position. Determine the principal angle in radians. Include a sketch.Example 2: Using a different quadrant than in Example 1 (but still not Quadrant 1), choose a reciprocal trig ratio. Determine all of the primary and reciprocal ratios for that angle, as well as the principal angle in radians.

Answer 1

Example 1:

The quadrants with their numbering (I, III,III, and IV) are shown below.

Now let us draw an angle in quadrant II.

We have drawn the angle above such that its measure from the positive x-axis is 135° . The angle 135° in radians is 3π/4.

Example 2:

Let us now choose an angle in the 3rd quadrant.