what is the exact value of cot(-270)

Question

what is the exact value of cot(-270)

Answer 1

270° is the angle that lies on the y-axis on a coordinate system, since each axis of rotation is 90°.  Being that the angle is negative, we rotate the angle 270 degrees clockwise from the positive x-axis about the origin.  This means that we will be on the positive y-axis.  On this axis, our coordinate is (0,1).  The x-coordinate is associated with cosine and the y-coordinate is associated with sine.

 

Remember that tanθ = sinθ / cosθ

 

Then cotθ = cosθ / sinθ

 

 

So,

 

cot(-270) = cos(-270) / sin(-270) = 0/1 = 0