Week 16 in Precalc 11

This week in math we learned about angles in standard form. First, we need to know some terminology. The rotation angle is the angle formed between the initial arm and the terminal arm. We would draw a sketch of this on a graph, that has the x-axis and the y-axis. This initial arm is the arm that is on the right side of the graph, this is where we always start when drawing a sketch. The terminal arm is the line you draw that represents the angle of the sketch you’re drawing. The initial arm is 0°, then as we move around counter-clockwise, the next arm at the top is 90°, then on the left, 180°, then at the bottom, 270° and back to the initial arm.

Standard position is when the initial arm is on the positive x-axis, the rotation is about the origin. The reference angle is that of the terminal arm and where it creates a right-triangle with the x-axis. We can use this right-triangle to find more information about it, using sine, cosine, tangent, and Pythagorean theorem. The reference angle can be found by adding or subtracting your rotation angle from the arm’s degree that is closest to it (e.g. 180° or 360°). This will make more sense when we look into an example. Quadrant I is the top right corner, quadrant II is the top left corner, quadrant III is the bottom left corner, and quadrant IV is the bottom right corner. You will need to know the quadrants to tell which quadrant an angle is in. Lastly, angles with the same terminal arm are co-terminal angles. These angles add to 360° when they are both positive, but don’t forget that one of the angles is always negative and the other is positive, so make sure if you subtract your rotation angle from 360, then add a negative sign to your answer.

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