Maths ALevel C3 help

Hey guys, does anyone know how to solve tan2x = -1? like how do you work out the values of x using this? Thanks!

That's C2 stuff, you have to tan^-1(-1) and double the range your given to get a set of solutions

That's C2 stuff, you have to tan^-1(-1) and double the range your given to get a set of solutions

you need to use the double angle formula for tan2x

you need to use the double angle formula for tan2x

Wait but when i do tan^-1(-1), i get 2x= -1/4 pi, however the answer in the book I am using says 2x=3/4 pi ?

What? That's not needed!



When you arctan (inverse tan) some value you will get $\tan(x) = a \Rightarrow x=\arctan(a)$ as the principle solution (meaning the closest one to 0). Depending on your interval, there are many more solutions since tan has a period of $\pi$ so you'll get grab more solutions as you keep adding or subtracting $\pi$ from your principle solution. So generally you get $x=\arctan(a) + n \pi$ where $n$ is some integer of your choice (principle solution is given when n=0)

In your case, notice how $-\frac{1}{4}\pi$ is your principle solution but $-\frac{1}{4}\pi + \pi = \frac{3}{4} \pi$, with $n=1$ here, hence the other solution.