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How do you show by substitution that the point (π /2, 1) lies on the curves of : $y = 2 sin (\frac{x}{3})$ $y=2sin(x/3)$ ?

1 Answer

Oct 6, 2015

Show that $(x, y) = (\frac{π}{2}, 1)$ $(x,y)=(pi/2,1)$ is a solution for $y = 2 sin (\frac{x}{3})$ $y=2sin(x/3)$ by substituting $\frac{π}{2}$ $pi/2$ for $x$ $x$ and solving for $y$ $y$

Explanation:

If
$XXX y = 2 sin (\frac{x}{3})$ $color(white)("XXX")y=2sin(x/3)$
when
$XXX x = \frac{π}{2}$ $color(white)("XXX")x=pi/2$
then
$XXX y = 2 sin (\frac{\frac{π}{2}}{3})$ $color(white)("XXX")y=2sin((pi/2)/3)$

$XXX = 2 sin (\frac{π}{6})$ $color(white)("XXX")=2sin(pi/6)$

$XXX = 2 \cdot \frac{1}{2}$ $color(white)("XXX")=2*1/2$

$XXX = 1$ $color(white)("XXX")=1$

Therefore $(\frac{π}{2}, 1)$ $(pi/2,1)$ is a solution for $y = 2 sin (\frac{x}{3})$ $y=2sin(x/3)$

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