Explain how to find the exact value of cot 5π/3, including quadrant location.
Question
Answer:
Start from the positive x-axis and move counterclockwise about the origin. You will first pass through Quadrant I, then Q II, then Q III, and so on. Convince yourself that the angle pi/3 is in Q I; 2 pi/3 is in Q II; 5 pi/3 is in Q IV. Because 5 pi/3 is in Q IV, its adjacent side is positive and its opposite side is negative.adj +1 1 sqrt(3) 1 sqrt(3)
cot 5pi/3 = --------- = ------------- = - ----------- = ------------- * ----------- = ------------
opp -sqrt(3) sqrt(3) sqrt(3) sqrt(3) 3
Note: If this is not completely clear to you, look up "special triangles" and look for a picture showing the hypotenuse, the adjacent side and the opposite side of the central angle. This is a "30-60-90 degree triangle" which has sides 1 and sqrt(3) and hypotenuse 2.
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10 months ago
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