The minimum value of cos theta + sin theta is | vedclass

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(B) Let $f(	heta) = \cos 	heta + \sin 	heta$.We can rewrite this as $f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos 	heta + \frac{1}{\sqrt{2}

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$-\sqrt{2}$

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(B) Let $f(	heta) = \cos 	heta + \sin 	heta$.We can rewrite this as $f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \cos 	heta + \frac{1}{\sqrt{2}} \sin 	heta ight) = \sqrt{2} \cos \left( 	heta - \frac{\pi}{4} ight)$.Since the range of the cosine function is $[-1, 1]$,we have $-1 \le \cos \left( 	heta - \frac{\pi}{4} ight) \le 1$.Multiplying by $\sqrt{2}$,we get $-\sqrt{2} \le \sqrt{2} \cos \left( 	heta - \frac{\pi}{4} ight) \le \sqrt{2}$.Thus,the minimum value of $f(	heta)$ is $-\sqrt{2}$.

The minimum value of $\cos \theta + \sin \theta$ is

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