Question

If `sin A = 3/4`, calculate sec A.

Answer 1

Given: `sin A = 3/4`

Step-wise calculation:

1. Use identity cos² A + sin² A = 1.

2. `cos A = ±sqrt(1 - sin^2 A)`

= `±sqrt(1 - (3/4)^2)`

= `±sqrt(1 - 9/16)`

= `±sqrt(7/16)`

= `±(sqrt(7))/4`

3. `sec A = 1/cos A`

= `± 1/((sqrt(7))/4)`

= `± 4/sqrt(7)`

= `± (4sqrt(7))/7`   ...(Rationalized)