Question

Pls help me answer this question

Answer 1

`(17)/(15)`

Explanation

sec x =
`(1)/(sinx)`

Which means

`(1)/(sin x) = (17)/(8)`

Flipping the fractions on both sides of the equation:

∴sin x =
`(8)/(17)`

With respect to the angle x:

hyp = Hypotenuse = 17 units

opp = Opposite = 8 units

∴adj = Adjacent can be determined using the Pythagorean Theorem:

`hyp^(2) = opp^(2) + adj^(2)`

`17^(2) = 8^(2) + adj^(2)`

`289 = 64 + adj^(2)`

`adj^(2) = 289 - 64`

Taking the square root on both sides to get rid of the square:

`adj = √(289 - 64)`

`= √(225)`

∴ Adjacent = 15 units

cos x =
`(adjacent)/(hypotenuse)`

=
`(15)/(17)`

∴csc x =
`(1)/(cos x)`

=
`(1)/((15)/(17))`

=
`(17)/(15)`