Question #d5791

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Answer 1 · 2017-04-05T07:37:18

$Y=-sqrt2sin(x+pi/4), or$

$Y=sqrt2sin(x+3pi/4).$

$Y=-sinx-cosx=-(sinx+cosx).$

$:. Y=-sqrt2(1/sqrt2sinx+1/sqrt2cosx)$

$=-sqrt2{sinxcos(pi/4)+cosxsin(pi/4)}$

$:. Y=-sqrt2sin(x+pi/4)$ .

If, $A$ is reqd. to be $+ve,$ then, we can rewrite $Y$ as,

$Y=sqrt2{(-1/sqrt2)sinx+(-1/sqrt2)cosx},$ so that,

$Y=sqrt2{sinxcos(3pi/4)+cosxsin(3pi/4)}, or,$

$Y=sqrt2sin(x+3pi/4).$

Enjoy Maths.!