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)

Algebra ->  Rational-functions -> 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)      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Since csc%28x%29=1%2Fsin%28x%29, the asymptotes are the zeros of the sine function.
x=0 and x=pi so
theta%2F2-pi%2F3=0 and theta%2F2-pi%2F3=pi
Solve these to get the equations of the asymptotes.
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There are no zeros for the csc function.
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Domain is all the values except for the two asymptotes locations from the first part.
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Since the range of the sine function is [-1,1], the range of the csc (its reciprocal) is (-infinity,-1]U[1,infinity). Since there is a multiplier in front of this function it directly multiplies the range.
(-infinity,-3%2F4]U[3%2F4,infinity).