# Math Help - Trigonometric Equation Confusion!?

1. ## Trigonometric Equation Confusion!?

The problem states:

solve the equation for the solution over the interval [0,360)

tanx - cotx = 0

the solution set according to the text book is:

{45, 135, 225, 315} which makes sense since these are the only values where x = y.

My question is how do you punch this into a calculator so it makes sense!? I keep getting oddball numbers other than 0!

2. Make sure your calculator is not set to radians. It has to be in degrees.

3. It is degree mode and when I punch in tan225 I get 1. But when I punch in cot225 I get 89.74535377.

4. I get that answer when I enter arctan(225)=89.7453537677, but if I enter tan(225) I get 1.

Also, I get cot(225)=1

5. on the calculator ...

$\cot(x) = \frac{1}{\tan(x)} \neq \tan^{-1}(x)$

6. Originally Posted by nee
The problem states:

solve the equation for the solution over the interval [0,360)

tanx - cotx = 0

the solution set according to the text book is:

{45, 135, 225, 315} which makes sense since these are the only values where x = y.

My question is how do you punch this into a calculator so it makes sense!? I keep getting oddball numbers other than 0!
You are using the answers given by the book. But do you know how to solve the given equation?

Here is one way.

tan(x) -cot(x) = 0
tan(x) -1/tan(x) = 0
Multiply both sides by tan(x),
tan^2(x) -1 = 0
tan^2(x) = 1
tan(x) = +,-1
x = arctan(1) or arctan(-1)
x = 45deg, 135deg, 225deg, 315deg