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Popular >

y= 1/2 cos(1/2 x-pi/6)

Solution

y = \frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6})

Solution

Period : 4 π

Domain : - \infty < x < \infty

Range : - \frac{1}{2} \leq f (x) \leq \frac{1}{2}

X Intercepts : (\frac{4 π}{3} + 4 πn, 0), (\frac{10 π}{3} + 4 πn, 0), Y Intercepts : (0, \frac{3}{4})

Asymptotes : None

Extreme Points : Maximum (\frac{π}{3} + 4 πn, \frac{1}{2}), Minimum (\frac{7 π}{3} + 4 πn, - \frac{1}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{2}, \frac{1}{2}]

Solution steps

Periodicity of

\frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6}) : 4 π

Domain of

\frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6}) : - \infty < x < \infty

Range of

\frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6}) : - \frac{1}{2} \leq f (x) \leq \frac{1}{2}

Axis interception points of

\frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6}) :

X Intercepts

: (\frac{4 π}{3} + 4 πn, 0), (\frac{10 π}{3} + 4 πn, 0),

Y Intercepts

: (0, \frac{3}{4})

Asymptotes of

\frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6}) :

None

Extreme Points of

\frac{1}{2} cos (\frac{1}{2} x - \frac{π}{6}) :

Maximum

(\frac{π}{3} + 4 πn, \frac{1}{2}),

Minimum

(\frac{7 π}{3} + 4 πn, - \frac{1}{2})

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Frequently Asked Questions (FAQ)

What is the y= 1/2 cos(1/2 x-pi/6) ?
The y= 1/2 cos(1/2 x-pi/6) is