Question

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

Answer 1

sin β = 1/9
sec β = 1/cos β
$cos \beta = \sqrt{1-( \frac{1}{9}) ^{2}} = \\ \sqrt{ \frac{80}{81} } = \\ \frac{4 \sqrt{5} }{9}$
$sec \beta = \frac{1}{ \frac{4 \sqrt{5} }{9} } = \frac{9}{4 \sqrt{5} }= \frac{9 \sqrt{5} }{20}$
sec β = 1.00623