Question

Explain this trig question to me?

Answer 1

Solve tan(x)(tan(x) - 1) = 0

The answer was x = +/- n(pi), x = pi/4 +/- n(pi)

Answer 2

I did tan(x) = 0 and got 0 and 2pi.
Then I did tan(x) = 1 and got pi/4 and 5pi/4.

Why did I go wrong on my answers?

Answer 3

if tan(x) = 0, then x = 0, x = pi, x = 2pi, etc

so in general, if tan(x) = 0, then x = pi*n where n is any integer

Answer 4

`Then I did tan(x) = 1 and got pi/4 and 5pi/4`
that is correct. But that's only 2 of infinitely many solutions

to capture ALL of the solutions, you need to add on multiples of pi to pi/4, which is why the "n(pi)" portion is added on. You don't need the plus minus because you can make n negative values to make things easier.

So if tan(x) = 1, then x = pi/4 + n*pi where n is any integer (positive or negative or 0)

Answer 5

I see exactly what you mean. That's for explaining that!