Find all solutions of the equation (tangent)

[LEG7930]

5tan(x)=18

so this is what I tried...

tan(x)=18/5

I have no problem doing these in a calculator, but then you get a decimal and I need exact answers, so do you guys have any suggestions on how to do these?

Along the same line I also was wondering how to solve the following:
tan(x)=4
tan(x)=5

If you can tell me how to do this with out a calculator i would GREATLY appreciate it

 

[Deleted member 4993]

5tan(x)=18

so this is what I tried...

tan(x)=18/5

I have no problem doing these in a calculator, but then you get a decimal and I need exact answers, so do you guys have any suggestions on how to do these?

Along the same line I also was wondering how to solve the following:
tan(x)=4
tan(x)=5

If you can tell me how to do this with out a calculator i would GREATLY appreciate it

How is your problem worded - exactly?

 

[LEG7930]

Find all solutions of the equation. (Enter each answer in the form ? + ?k, 0 ? ? < 2?.)

 

[galactus]

\(\displaystyle tan(\frac{18}{5})=\frac{\pi}{2}-tan^{-1}(\frac{5}{18})\)

The others can be written similarly.

In general, \(\displaystyle \frac{\pi}{2}-tan^{-1}(\text{reciprocal})\)