Question

If sin y° = a/6 and tan y° = a/b what is the value of sec y°

Answer 1

`sec\ y = (6)/(b)`

Explanation:

Given

`sin\ y = (a)/(6)`

`tan\ y = (a)/(b)`

Required

sec y

From trigonometry;

`sec\ \theta = tan\ \theta\ /\ sin\ \theta`

Substitute y for θ

`sec\ y= tan\ y\ /\ sin\ y`

Substitute values for tan y and sin y

sec y = a/b ÷ a/6

`sec\ y= (a)/(b) /\ (a)/(6)`

`sec\ y= (a)/(b) *\ (6)/(a)`

`sec\ y= (6 * a)/(a *b)`

`sec\ y= (6 a)/(ab)`

Divide numerator and denominator by a

`sec\ y= (6)/(b)`

Hence, the value of sec y is

`sec\ y= (6)/(b)`