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Using reference angles to evaluate trig function

  1. Jan 12, 2018 #1
    Mod note: Moved from a Homework section, as this is more of a conceptual question than an actual homework problem.
    I can't really memorize the unit circle, but I do remember my instructor teaching us how to use reference angles to evaluate any trig function without needing the unit circle. I was wondering if anyone remembers this method? I tried to google it but couldn't really find any good results on the topic.

    I know we had to memorize three triangles for a 45, 60, 90 degree angles, but I'm a bit lost after that.

    @Sparkle, if you post a question in the Homework sections, you must use the homework template.
    Last edited by a moderator: Jan 12, 2018
  2. jcsd
  3. Jan 12, 2018 #2


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    Once you understand the 45-45-90 and 30-60-90 triangles, use the method described here:
  4. Jan 12, 2018 #3


    Staff: Mentor

    The angles also include 0 and 30 degrees.

    You can evaluate any trig function of the listed angles (including the ones I added), using the unit circle and a bit of geometry. For example, since the terminal ray for 120° is the reflection across the vertical axis of the ray for 60°, it follows that sin(120°) = sin(60°) and that cos(120°) = - cos(60°). You can repeat this kind of analysis for any angle that can be obtained by reflecting the terminal rays for 30°, 45°, 60°, or 90°, and use it to find any of the trig functions of these angles.
  5. Jan 30, 2018 #4
    Hey, thank you guys! It has been a while since this post, and I'm now getting to figuring this out. They loaded us up with school work to weed out the weak for the full-refund drop date, plus I was handed a pretty big project at work. Anyway, I'll get back with my results on these methods. Also, I may have posted in the homework section (sorry about that if I did), but this isn't really homework per say but something I should already know by now.
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