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Answer on Trigonometry Question for maria pretty

Question #5448
Hello Dear Expert what isthe greatest value of "sin theta +cos theta"
Expert's answer
the first step – take the first derivative of the function (sin theta + cos theta):
d f / d theta = -cos theta + sin theta =>
=> in max/min point d f / d theta = 0 =>
=> sin theta = cos theta => divide both parts by cos theta => tg theta = 1 =>
=> theta = pi/4 + n*pi, where n – integer =>

=> so we have theta = 450, sin 450 = (sqrt(2)/2), cos 450 =(sqrt(2)/2), sin 450 + cos 450 = sqrt(2) ≈ 1,414

Check if theta = 450 is not the minimum point, take the other value of theta = 00, sin 0 + cos 0 = 0 + 1 = 1 < sqrt(2), thus greatest value of (sin theta + cos theta = 1.414)

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