Question

Given sin A = 4/5 and cos A < 0, find tan A

Answer 1

tan A = -
`(4)/(3)`

Explanation:

Using the identity sin² A + cos² A = 1, then

(
`(4)/(5)` )² + cos² A = 1

`(16)/(25)` + cos² A = 1 ( subtract
`(16)/(25)` from both sides )

cos² A =
`(9)/(25)` ( take the square root of both sides )

cos A = ±
`\sqrt{(9)/(25) }` and given cosA < 0, then

cos A = -
`(3)/(5)`

Using the identity

tan A =
`(sinA)/(cosA)`, then

tan A =
`((4)/(5) )/(-(3)/(5) )` =
`(4)/(5)` × -
`(5)/(3)` = -
`(4)/(3)`