# Thread: solutions for tan and sin

1. ## solutions for tan and sin

I am working on a few problems for a test tommorrow and I would like to know if Tan(x/3)= 3.8 and 2sin3x=cosx can be solved by putting tan(x/3) in y1 and 3.8 in y2 or is there a better way? The study sheet tells me to find all solutions to 3 decimals. I would appreciate any method you could provide.
Thank you!
Keith Stevens

2. Originally Posted by kcsteven
I am working on a few problems for a test tommorrow and I would like to know if Tan(x/3)= 3.8 and 2sin3x=cosx can be solved by putting tan(x/3) in y1 and 3.8 in y2 or is there a better way? The study sheet tells me to find all solutions to 3 decimals. I would appreciate any method you could provide.
Thank you!
Keith Stevens
I'm not clear on what your question is. You have two equations to solve for x, but your reference to y1 and y2 sounds like you are graphing them together somehow?

The only way I know how to solve $\displaystyle tan(x/3) = 3.8$ would be to use a calculator to get a numerical estimate: $\displaystyle x = 3 \cdot tan^{-1}(3.8)$. Another way (perhaps this is what you were trying to get at) would be to graph the two functions:
$\displaystyle y = tan(x/3)$
$\displaystyle y = 3.8$
simultaneously and find the points of intersection on the graphics screen.

An alternate way of getting a "graphical" solution would be to graph
$\displaystyle y = tan(x/3) - 3.8$ and use the "zeros" function on your calculator.

You can sort of solve $\displaystyle 2sin(3x)=cos(x)$ analytically, that is to say that you can do some work with the equation before you approximate the solution. (Expand the sin(3x) and write everything in terms of just sin(x) and this will give you a 6th degree polynomial in sin(x). Then numerically approximate the solution.) Probably the best way is to graph:
$\displaystyle y = 2sin(3x)$
$\displaystyle y = cos(x)$
and look for intersection points.

-Dan