SOLUTION: Without graphing, give the domain, range, zeros, and equation of vertical asymptotes of the following function.
f(θ）=3/4csc(θ/2-π/3)
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Question 1082390: Without graphing, give the domain, range, zeros, and equation of vertical asymptotes of the following function.
f(θ）=3/4csc(θ/2-π/3)
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Since , the asymptotes are the zeros of the sine function.
and so
and
Solve these to get the equations of the asymptotes.
.
.
There are no zeros for the csc function.
.
.
Domain is all the values except for the two asymptotes locations from the first part.
.
.
Since the range of the sine function is [-1,1], the range of the csc (its reciprocal) is (,]U[,). Since there is a multiplier in front of this function it directly multiplies the range.
(,]U[,).
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