Gennaio 21, 2020

Come si semplifica $sin (\frac{π}{6} + x)$ $Sin (pi / 6 + x)$ ?

Risposta:

$\frac{1}{2} cos x + \frac{\sqrt{3}}{2} sin x$ $1/2cosx+sqrt3/2sinx$

Spiegazione:

Using the appropriate $Addition formula$ $color(blue)" Addition formula "$

$∣ ∣ ∣ ∣ ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ \frac{a}{a} sin (A \pm B) sin A cos B \pm cos A sin B \frac{a}{a} ∣ ∣ - --------------------------------- -$ $color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A±B)sinAcosB±cosAsinB)color(white)(a/a)|)))$

then $sin (\frac{π}{6} + x) = sin (\frac{π}{6}) cos x + cos (\frac{π}{6}) sin x$ $sin(pi/6+x)=sin(pi/6)cosx+cos(pi/6)sinx$

Using the $exact value triangle for this angle$ $color(blue)" exact value triangle ""for this angle"$

Then $sin (\frac{π}{6}) = \frac{1}{2} and cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ $sin(pi/6)=1/2" and " cos(pi/6)=sqrt3/2$

$\Rightarrow sin (\frac{π}{6} + x) = \frac{1}{2} cos x + \frac{\sqrt{3}}{2} sin x$ $rArrsin(pi/6+x)=1/2cosx+sqrt3/2sinx$

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