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Popular >

y= 1/5 cos(1/2 x-pi/8)

Solution

y = \frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8})

Solution

Period : 4 π

Domain : - \infty < x < \infty

Range : - \frac{1}{5} \leq f (x) \leq \frac{1}{5}

X Intercepts : (\frac{5 π}{4} + 4 πn, 0), (\frac{13 π}{4} + 4 πn, 0), Y Intercepts : (0, \frac{2 + 2}{10})

Asymptotes : None

Extreme Points : Maximum (2 arctan (2 - 1) + 4 πn, \frac{1}{5}), Minimum 2 arctan (2 - 1) + 2 π + 4 πn, \frac{cos ( \frac{8 a r c t a n ( 2 - 1 ) + 7 π}{8} )}{5}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{5}, \frac{1}{5}]

Solution steps

Periodicity of

\frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8}) : 4 π

Domain of

\frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8}) : - \infty < x < \infty

Range of

\frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8}) : - \frac{1}{5} \leq f (x) \leq \frac{1}{5}

Axis interception points of

\frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8}) :

X Intercepts

: (\frac{5 π}{4} + 4 πn, 0), (\frac{13 π}{4} + 4 πn, 0),

Y Intercepts

: (0, \frac{2 + 2}{10})

Asymptotes of

\frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8}) :

None

Extreme Points of

\frac{1}{5} cos (\frac{1}{2} x - \frac{π}{8}) :

Maximum

(2 arctan (2 - 1) + 4 πn, \frac{1}{5}),

Minimum

2 arctan (2 - 1) + 2 π + 4 πn, \frac{cos ( \frac{8 a r c t a n ( 2 - 1 ) + 7 π}{8} )}{5}

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Frequently Asked Questions (FAQ)

What is the y= 1/5 cos(1/2 x-pi/8) ?
The y= 1/5 cos(1/2 x-pi/8) is