# Math Help - Solving trigonometric equatio

1. ## Solving trigonometric equatio

I have to solve X within the domain 0 deg ≤ X ≤ 360 deg (X = pheta (degrees))

1) tan X = -1
2) sin X = -1/2
3) cos X = 0
4) cos X = -1/2

Thank you.

2. ## Re:

You trigonometric inverses and then multiply by (180/pi)

3. Originally Posted by tom_asian
1) tan X = -1
$\tan x=-1\implies x=\arctan(-1)$

Does that make sense?

Do the same with the others.

4. These are fundamental trigonometric equations.
$\sin x=a\Rightarrow x=(-1)^k\arcsin a+k\pi,k\in\mathbf{Z}$
$\cos x=b\Rightarrow x=\pm\arccos b+2k\pi,k\in\mathbf{Z}$
$\tan x=c\Rightarrow x=\arctan c+k\pi,k\in\mathbf{Z}$
Then find the values of $k$ for which $0\leq x\leq 2\pi$ and then multiply by $\displaystyle\frac{180}{\pi}$

5. by the way, it's "theta"

did you get the questions done ok?

6. Originally Posted by Jhevon
by the way, it's "theta"

did you get the questions done ok?
I can do the questions now. thanks.. although i dont know what is "arc"

7. Originally Posted by tom_asian
I can do the questions now. thanks.. although i dont know what is "arc"
"arc" as it is used here just means "inverse"

so arctan(x) means the inversed tangent of x or as you may know it as $\tan ^{-1}x$

8. ## Re:

Re:

9. Originally Posted by qbkr21
Re::d
ahh... thanks..

so thats another way to call it. I just call it sin inverse, etc....

10. Originally Posted by tom_asian
ahh... thanks..

so thats another way to call it. I just call it sin inverse, etc....
yes