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Popular >

y= 2/3 sin(x)

Solution

y = \frac{2}{3} sin (x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{2}{3} \leq f (x) \leq \frac{2}{3}

X Intercepts : (2 πn, 0), (π + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{2} + 2 πn, \frac{2}{3}), Minimum (\frac{3 π}{2} + 2 πn, - \frac{2}{3})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{2}{3}, \frac{2}{3}]

Solution steps

Periodicity of

\frac{2}{3} sin (x) : 2 π

Domain of

\frac{2}{3} sin (x) : - \infty < x < \infty

Range of

\frac{2}{3} sin (x) : - \frac{2}{3} \leq f (x) \leq \frac{2}{3}

Axis interception points of

\frac{2}{3} sin (x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{2}{3} sin (x) :

None

Extreme Points of

\frac{2}{3} sin (x) :

Maximum

(\frac{π}{2} + 2 πn, \frac{2}{3}),

Minimum

(\frac{3 π}{2} + 2 πn, - \frac{2}{3})

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