# Show that f is continuous on (-infty , infty). f(x)={(sin(x) if x<pi/4),(cos(x) if xge pi/4):}

Show that f is continuous on $\left(-\mathrm{\infty },\mathrm{\infty }\right)$.
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Coleman Ali
you know that the sine ans cosine functions are continuousbecause all the regions of the graph are defined...the only problemis the transition between the two function at $\pi /4$
so you would have to prove that $\mathrm{sin}\left(\pi /4\right)=\mathrm{cos}\left(\pi /4\right)$
since $\mathrm{sin}\left(\pi /4\right)=\mathrm{cos}\left(\pi /4\right)=\sqrt{2}/2=0.7071$
where one functions ends, the other begins, making thetransition seamless and thus, it is a continuous functions.