Question

What are the x-intercepts for:

y= sin πx + cos πx ???

Answer 1

http://www.math.tamu.edu/~Marcia.Drost/150lect75b.pdf

Answer 2

thanks!

Answer 3

\(\bf y = sin(\pi x)+cos(\pi x)\implies 0= sin(\pi x)+cos(\pi x)\\ \quad \\
-sin(\pi x)=cos(\pi x)\implies sin(-\pi x)=cos(\pi x)\\ \quad \\
sin(-\pi x)=cos(-\pi x)\implies sin^2(-\pi x)=cos^2(-\pi x)\\ \quad \\
sin^2(-\pi x)-cos^2(-\pi x)=0\implies sin(-2\pi x) = 0\\ \quad \\

sin^{-1}(sin(-2\pi x)) = sin^{-1}(0)\implies -2\pi x= sin^{-1}(0)\)