Answer to Question #159367 in Calculus for effa

Question

find $y$, when $y= sin x - cos x$

Answer 1

Solution:

$The\:compound\:periodicity\:of\:the\:sum\:of\:periodic\:functions\:is\:the\:least\:\\common\:multiplier\:of\:the\:periods$

$Periodicity\;of\;sin(x):\;2\pi\\Periodicity\;of\;cos(x):\;2\pi$

$\mathrm{Domain\:of\:}\:\sin \left(x\right)-\cos \left(x\right)\::\begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Range\:of\:}\sin \left(x\right)-\cos \left(x\right):\\\begin{bmatrix}\mathrm{Solution:}\:&\:-\sqrt{2}\le \:f\left(x\right)\le \sqrt{2}\:\\ \:\mathrm{Interval\:Notation:}&\:\left[-\sqrt{2},\:\sqrt{2}\right]\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:\sin \left(x\right)-\cos \left(x\right):\quad \mathrm{X\:Intercepts}:\:\left(\frac{\pi }{4}+2\pi n,\:0\right),\:\left(\frac{5\pi }{4}+2\pi n,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-1\right)$