Question 172027
I have two questions that I am stuck on. Will you please help me.
1. Find the exact value of cot(-pi/6)
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The tan and cot are + - + - in quadrants I II II and IV.  pi/6 is 30 degs, so -30 degs is in quadrant 4.  The cot(-30) is negative, viewed as either cot(330) or -cot(30), either way.
The cot is cos/sin.  The sin of 30 degs is 1/2, and the cos in sqrt(3)/2.  (Can you use those, or do you need a proof?)
cot(-30) = -(sqrt(3)/2)/(1/2) = -sqrt(3)
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2. Find the exact value of: sin 405 degrees
Trig functions are cyclic with a 360 deg cycle.  You can subtract 360 from the angle any number of times, until it's less than 360.  In this case, 405-360 = 45 degs
The sin(45) = sqrt(2)/2