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