How do you evaluate the sine, cosine, tangent, cosecant, secant, And cotangent of t=-pi/2?

1 Answer
Dean R.
Apr 24, 2018

#cos(-pi/2) = 0#

#sin(-pi/2) = -1#

#cot(-pi/2) = 0#

#csc(-pi/2)=-1#

with #tan(-pi/2)# and sec#(-pi/2)# undefined.

Explanation:

That corresponds to rectangular coordinate #(0, -1)#, so an "adjacent" of #x=0#, an "opposite" of #y=-1# and a hypotenuse of #r=sqrt{0^2 + (-1)^2}=1#.

We apply the usual ratios to get our trig functions:

#cos(-pi/2) = x/r = 0#

#sin(-pi/2) = y/r = -1#

#tan(-pi/2)=y/x = -1/0 # which is UNDEFINED.

#cot(-pi/2) = x/y = 0#

#csc(-pi/2)=r/y=-1#

#sec(-pi/2)=r/x = 1/0 # which is undefined

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