Evaluate the remaining trigonometric functions? CSC x is undefined, cos x <0

1 Answer
Apr 16, 2018

#sinx=0#, #cosx=-1#, #tanx=0#, #cotx=#undefined #secx= -1#

Explanation:

If cosecant is undefined, that means it is over #0#. Remember that cosecant is hypotenuse over opposite side (reciprocal of sine). Hypotenuse is #1#, so sine should be #0/1#, or #0#.

#sin^2x+cos^2x=1#

#0^2x+cos^2x=1#

#cos^2x=1#

#cosx=+-1 rarr# Disregard the positive #1# because the question says that #cosx<0#.

#cosx=-1#

#tanx=sinx/cosx#

#0/-1=0#

Tangent is #0#.

#cotx=cosx/sinx#

#(-1)/0=#undefined

Cotangent is undefined.

Secant is reciprocal of cosine:
#secx= 1/cosx= 1/-1= -1#