Answer to Question #5448 in Trigonometry for maria pretty

Question

Hello Dear Expert what isthe greatest value of "sin theta +cos theta"

Answer 1

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)