What is evaluate sin (-t) and csc(-t) if sin(t)=-2/5?

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Answer 1 · 2018-02-23T18:27:58

#sin(-t)=2/5# #csc(-t)=5/2#

Recall that #sin(x)# is an odd function, meaning that #sin(-x)=-sin(x).#

So, this means that #sin(-t)=-sin(t)#

We already know that #sin(t)=-2/5#, so #sin(-t)=-sin(t)=-(-2/5)=2/5#.

#csc(t)=1/sin(t)#

#csc(-t)=1/sin(-t)#

We just calculated #sin(-t)#:

#csc(-t)=1/(2/5)=5/2# (Remember, #1/(a/b)=b/a#).