Question

Find the missing values given that cos(theta) = 1.

Answer 1

We know that
cos(theta) = 1---------> the value of cos is positive
then
angle  theta------> could be in the first or fourth quadrant

Part 1) find sin theta
sin² theta+cos² theta=1------> sin² theta=1-cos² theta----> 1-1²----> 0
sin theta=0

Part 2) find csc theta
csc theta=1/sin theta
but sin theta =0
therefore
csc theta-------> it does not exist, it is not defined

Part 3) find sec theta
sec theta=1/cos theta
cos theta=1
so sec theta=1/1----> sec theta=1

Part 4) find cot theta
cot theta=cos theta/sin theta
but sin theta=0
therefore
cot theta-------> it does not exist, it is not defined