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-( (1)/(9)) ^(2)} = \\ \sqrt{ (80)/(81) } = \\ (4 √(5) )/(9)`

`sec \beta = (1)/( (4 √(5) )/(9) ) = (9)/(4 √(5) )= (9 √(5) )/(20)`
sec β = 1.00623