What I learned this week in trigonometry was how to find reference angles. It is important to know this because it is a basic thing to know and continue to use throughout trigonometry.

How I learned to find the reference angle is through the rotation angle. The rotation angle is the angle formed between the initial arm and the terminal arm. The reference angle is the acute angle formed between the initial arm of the rotation angle and the x-axis.

To find the reference angle it depends on which quadrant (Q) the rotation angle is in. If it is in Q 1, the reference angle is the rotation angle. Q2, you minus the rotation angle from 180°. Q3, minus 180° from the rotation angle. Q4, 360° minus the rotation angle.

To find the reference angle in question a) first you want to determine what quadrant the angle is in from the rotation angle, in this case Q4 and draw an angled line from the middle of the grid to represent the rotation angle. Once you have done that, draw the angle that connects the line you created to the x-axis, this is the reference angle. Next draw an arrow that starts at the terminal arm, and ends at the angled line, this is the rotation. Since the rotation angle is in Q4, you will minus the rotation angle 313° from 360° because 360° is the x-axis angle the rotation angle is attached too. Your final answer will be 47°.

First step to find the reference angle in question b) is to draw the rotation line in the correct quadrant. From there draw the angle that connects the line to the x-axis, this is the angle you are trying to find. Draw the arrow that starts at the terminal angle and ends and the rotation angle, this represents the rotation. Since the rotation angle is in Q3, you will minus the x-axis angle the rotation angle just passed, 180°, from the rotation angle 230°. Your final answer will be 50°.