Question

If sin=3/5 then what does tan equal

Answer 1

Answer:
`tan(x)=\±(3)/(4)`

Explanation:

You know that
`sin(x)=(3)/(5)` and you can identify that. Then:

`sin^2(x)=((3)/(5))^2`

`sin^2(x)=(9)/(25)`

Remember that:

`cos^2(x)=1-sin^2(x)`

Then
`cos^2(x)` is:

`cos^2(x)=1-(9)/(25)\\\\cos^2(x)=(16)/(25)`

Apply square root to both sides to find cos(x):

`√(cos^2(x))=\±\sqrt{(16)/(25)}\\cos(x)=\±(4)/(5)`

Remember that:

`tan(x)=(sin(x))/(cos(x))`

Then, this is:

`tan(x)=((3)/(5))/(\±(4)/(5))`

`tan(x)=\±(3)/(4)`