Question 749108: Just started summer Trig review for pre-calc/ Calc. Could be going better.
I understand that S = R where S = 1, but they are using real numbers now in terms of 't' and I'm unsure. The question asks...
"Sketch the oriented arc on the unit circle corresponding to each of the following real numbers."
1.) t = 3pi/4 (which I got; 135 degrees counter clockwise, Quadrant II angle)
2.) t = -2pi (also good; 1 full rotation clockwise, quadrilateral angle)
3.) t = -2 (lost me)
4.) t = 117 (same issue as the last).
-How do I handle regular old numbers in these scenarios?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 1.) t = 3pi/4 (which I got; 135 degrees counter clockwise, Quadrant II angle)
2.) t = -2pi (also good; 1 full rotation clockwise, quadrilateral angle)
3.) t = -2 (lost me)
4.) t = 117 (same issue as the last).
***
3π/4, -2π, -2, and 117 are in radians which are real numbers as you said.
To illustrate:
1.) t = 3pi/4 =2.3532..radians=135º
2.) t = -2pi=-6.28 radians=0
3.) t = -2=-2 radians=-2/π*180≈-114.59º
4.) t = 117=117 radians=117/π*180≈6703.61º
note:special angles like 30º, 60º, 45º, etc are written in terms of π for ease of calculation and explanation but angles in-between are expressed as real numbers without π.
Hope this helps.
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