tan squared- tanx-6=0 the interval is 0 degrees<x<360 degrees?

Answer 1

Rewriting:
(tan x)^2 - tan x - 6 = 0
(tan x - 3)(tan x + 2) = 0

tan x - 3 = 0
tan x = 3
x = 71.57

tan x + 2 = 0
tan x = -2
x = 296.57

Answer 2

To solve an algebraic problem like this, using the method called substitution may help, where you substitute a "dummy symbol" to simplify the problem. Substitution is used when you see a complicated expression repeated, to help you more clearly identify a solution.

In this case:
1) you can substitute U for tan x to get: U^2 - U - 6 = 0
2) then factor using the FOIL method to get the roots of U.
3) Then replace U with the original expression (tan x), and solve for x. You should get two solutions.

You might run into trouble when you have the expression "tan x = blah" but try drawing a graph of y = tan x for values between 0 < x < 360 (or look it up - you may have it in your text book) and look for the values of x where tan x is equal to blah.