März 13, 2020

von Charita

Wie vereinfacht man $sin (\frac{π}{6} + x)$ $Sin (pi / 6 + x)$ ?

Antworten:

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

Erläuterung:

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

$color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A±B)sinAcosB±cosAsinB)color(white)(a/a)|)))$

then $sin(pi/6+x)=sin(pi/6)cosx+cos(pi/6)sinx$

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

Then $sin(pi/6)=1/2" and " cos(pi/6)=sqrt3/2$

$rArrsin(pi/6+x)=1/2cosx+sqrt3/2sinx$