De6j6ascanorses
De6j6ascanorses De6j6ascanorses
  • 02-09-2016
  • Mathematics
contestada

Suppose sin(β) = 1/9. Find the exact value of sec(β) for 0 < β

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HomertheGenius
HomertheGenius HomertheGenius
  • 11-09-2016
sin β = 1/9
sec β = 1/cos β
[tex]cos \beta = \sqrt{1-( \frac{1}{9}) ^{2}} = \\ \sqrt{ \frac{80}{81} } = \\ \frac{4 \sqrt{5} }{9} [/tex]
[tex]sec \beta = \frac{1}{ \frac{4 \sqrt{5} }{9} } = \frac{9}{4 \sqrt{5} }= \frac{9 \sqrt{5} }{20} [/tex]
sec β = 1.00623


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