Find Terminal Point on Unit Circle by using Reference Angle
In these examples, in radian measure, we must compute the reference angle. We write in the quadrantal angles to help us place the given angle in the correct quadrant. Then we draw in the reference angle to the x-axis. To compute the reference angle, we set up the appropriate subtraction and get a common denominator when necessary. We then substitute the reference angle into the trig functions (sine and cosine) and are very careful to include the correct sign (positive/negative) in front. To make this determination, we use the phrase "All Students Take Calculus" to determine if our trig function will be positive or negative based on the original angle and its quadrant. After we use our reference angle, the computations are fairly easy as they turn out to be "nice" angles that come up quite often in trigonometry. To create the terminal point on the unit circle, we must remember that cosine=x-value while sine=y-value (cos(t),sin(t)).
This video contains examples that are from Algebra and Trigonometry, 1st ed, by Abramson, Belloit, Falduto, Gross, Lippman et al. It is an open-source textbook from OpenStax that you may download for free at https://openstax.org/details/books/al.... The text is licensed under the Creative Commons Attribution license. https://creativecommons.org/licenses/...
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