## En one year ago HELP! please prove that Arctan(-x)= - Arctanx

1. zepdrix

I'd prolly just do the same thing as the last one :o$\large\rm y=-\arctan(x)$$\large\rm -y=\arctan(x)$$\large\rm \tan(-y)=x$Since tangent is an odd function,$\large\rm \tan(-y)=-\tan(y)=x$$\large\rm \tan(y)=-x$$\large\rm y=\arctan(-x)$

2. zepdrix

Lot of weird little steps in that though :D

3. En

thanks :)))

4. En

@zepdrix what do you mean to that the tangent is an odd function?

5. zepdrix

An odd function satisfies this property:$\large\rm f(-x)=-f(x)$Examples:$\large\rm f(x)=x^3$$\large\rm f(-x)=(-x)^3=-(x)^3=-f(x)$ $\large\rm g(x)=\sin(x)$$\large\rm g(-x)=\sin(-x)=-\sin(x)=-g(x)$ An even function satisfies this property:$\large\rm f(-x)=f(x)$Examples:$\large\rm f(x)=x^2$$\large\rm f(-x)=(-x)^2=(x)^2=f(x)$ $\large\rm g(x)=\cos (x)$$\large\rm g(-x)=\cos(-x)=\cos(x)=g(x)$

6. zepdrix

Tangent is like sine in this respect.

7. zepdrix

It's good to have an understanding of even and odd functions, but at the very least make sure you understand the basics that it allows us with trig functions: if you have a negative in your cosine, it can disappear if you have a negative in your sine or tangent, it can come outside

8. En

oh my goodness.. thank you so much