Mirandaregina
  • Mirandaregina
If sec (π/2 – theta) = (√3)/2, what is csc theta? So far I have that theta = (π - √3)/2, but I don’t know how to use that to find csc theta.
Mathematics
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katieb
  • katieb
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phi
  • phi
are you sure it says sqr(3)/2 and not 2/sqr(3) ?
Mirandaregina
  • Mirandaregina
@phi yes
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phi
  • phi
sec is 1/cos sec(90-x) = 1/cos(90-x) cos(90-x) = cos(90)cos(x) + sin(90)sin(x) = 0+1*sin(x)= sin(x) so sec(90-x)= 1/sin(x)

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phi
  • phi
so we are told \[ \frac{1}{\sin(x)}= \frac{\sqrt{3}}{2} \\ \sin x = \frac{2}{\sqrt{3}} \] the problem is 2/sqrt(3) is about 1.1547 and the max sin can ever be is 1
phi
  • phi
however, if we ignore that detail then \[ \frac{1}{\sin(x)}= \csc(x)= \frac{\sqrt{3}}{2} \] and the answer is sqr(3)/2
Mirandaregina
  • Mirandaregina
@phi thank you for explaining this

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