How-do-you-find-the-interval-in-which-x-belongs-such-that-sinx-cosx-sinx-cosx-

Question Number 134538 by bemath last updated on 05/Mar/21

How do you find the interval in which x belongs such that |sinx+cosx|=sinx + cosx?

Answered by EDWIN88 last updated on 05/Mar/21

let \sin x + \cos x = y \Rightarrow we get equation ∣ y ∣ = y

this equation satisfied if only if y ⩾ 0

since \sin x + \cos x = \sqrt{2} \sin (x + \frac{π}{4}) we get

\Rightarrow \sqrt{2} \sin (x + \frac{π}{4}) ⩾ 0, \sin (x + \frac{π}{4}) ⩾ 0

note that sine function be ⩾ 0 in first and

2^{nd} quadrant so 0 ⩽ x + \frac{π}{4} ⩽ π; or

- \frac{π}{4} + 2 k π ⩽ x ⩽ \frac{3 π}{4} + 2 k π .

Commented by EDWIN88 last updated on 05/Mar/21

Commented by EDWIN88 last updated on 05/Mar/21

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