Question

Please explain your answer, thanks.

Answer 1

tan x = -
`(3√(7) )/(7)`

Explanation:

sin²x + cos²x = 1

cos²x = 1 - sin²x

cos x = ± √( 1 - sin²x )

tan x =
`(sinx)/(cosx)`

~~~~~~~~~~~~~~~~~~~

sin x =
`(3)/(4)` and cos x < 0

tan x - ?

cos x = -
`\sqrt{1 -((3)/(4))^2 }` = -
`(√(7) )/(4)`

tan x =
`(3)/(4)` ÷ ( -
`(√(7) )/(4)` ) = -
`(3)/(4)` ×
`(4)/(√(7) )` = -
`(3√(7) )/(7)`