SOLUTION: Find the exact value of cot(-315º). Thank You

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Question 42332: Find the exact value of cot(-315º).
Thank You
Answer by psbhowmick(489) About Me  (Show Source):
You can put this solution on YOUR website!
METHOD TO BE FOLLOWED BY SOMEONE WHO IS NEW TO THIS TYPE OF PROBLEMS


First, let us find the quadrant in which the angle -315%5Eo lies.

-315 = 3 x (-90) -45
(-90) refers to clockwise rotation from axis OX to OY'.
2 x (-90) refers to clockwise rotation from axis OX to OX'.
3 x (-90) refers to clockwise rotation from axis OX to OY.
So, any further clockwise rotation less than 90%5Eo keeps the radius vector in the 1st quadrant.

(-45) refers to further 45%5Eo clockwise rotation from OY.
See th figure below.
drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Aline%280%2C0%2C8%2C8%29%2C%0D%0Agreen%28line%288%2C0%2C8%2C8%29%29%2C%0D%0Agrid%281%29%2C%0D%0Alocate%288%2C8%2CP%29%2C%0D%0Alocate%288%2C0%2CA%29%2C%0D%0Alocate%280%2C0%2CO%29%0D%0A%29

cot%28-315%5Eo%29 = cot(< AOP) = OA%2FAP = 1
[since both OA and AP are along positive x-axis and positive y-axis respectively so both are positive]


METHOD TO BE FOLLOWED BY SOMEONE WHO IS NOT NEW TO THIS TYPE OF PROBLEMS

cot%28-315%5Eo%29
= cot%28360%5Eo-45%5Eo%29
= cot%2845%5Eo%29
= 1