Assuming that you meant , then yes, you have the right idea.
However, does not have an exact surd value, so if you are asked to keep your answer exact, you would not give a decimal approximation for this.
I have the equation y = -2 tan (3x + 180) + 3
I need to find the x-intercepts. To do this, I know that I need to set y to equal 0 and then solve for x.
This is what I've done:
y = -2 tan (3x + 180) + 3
-3 = -2 tan (3x + 180)
3/2 = tan (3x + 180)
At this point I'm stuck. I don't know how to further isolate the x. Can I do this??
tan ^-1 3/2 = 3x + 180, solve for tan ^-1 3/2 and continue isolating x?
Okay, great... but how do I list zeros for this then?
Or, do I just write:
Roots: x = (tan^-1 (3/2) - 180)/3 ?
When I solve for x using the decimal value of tan^-1 (3/2) I get -41.23002251, but that is only one root, and there has to be more than one.
Can I take that number and just add intervals of 60 degrees since the vertical asymptotes are set at intervals of 60 degrees?
Yes; all the x-intercepts would be given by , because remember, is any integer. So you would get a different solution for each different value of .
To get specific x-intercepts, you would just need to specify what you are using. For example, gives:
I hope that this helps.