How do you find the quadrants in which the terminal side of #theta# must lie given #costheta# and #cottheta# have the same sign?

1 Answer
Dec 22, 2017

Answer:

If #cos(theta)# and #cot(theta)# have the same sign, then the terminal side of #theta# must be in QI or QII.

Explanation:

#cos(theta)# is positive anywhere #x>0#, so QI and QIV.
#cos(theta)# is negative when #x<0#, so in QII and QIII.

#cot(theta)# is positive anywhere #x# and #y# have the same sign, so QI and QIII.
#cot(theta)# is negative when #x# and #y# have opposite signs, so QII and QIV.

From this we know #cos(theta)>0# and #cot(theta)>0# in QI.
Both #cos(theta)# and #cot(theta)# are negative in QII.