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Popular >

f(x)=sin(2x)cos(x)

Solution

f (x) = sin (2 x) cos (x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - \frac{2}{3} sin (2 (- arccos (- \frac{2}{3}) + 2 π)) \leq f (x) \leq \frac{4}{3 3}

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum (arccos (\frac{2}{3}) + 2 πn, \frac{4}{3 3}), Minimum (\frac{π}{2} + 2 πn, 0), Maximum (arccos (- \frac{2}{3}) + 2 πn, \frac{4}{3 3}), Minimum (- arccos (- \frac{2}{3}) + 2 π + 2 πn, - \frac{2}{3} sin (2 (- arccos (- \frac{2}{3}) + 2 π))), Maximum (\frac{3 π}{2} + 2 πn, 0), Minimum (2 π - arccos (\frac{2}{3}) + 2 πn, \frac{2}{3} sin (2 (2 π - arccos (\frac{2}{3}))))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{2}{3} sin (2 (- arccos (- \frac{2}{3}) + 2 π)), \frac{4}{3 3}]

Solution steps

Periodicity of

sin (2 x) cos (x) : 2 π

Domain of

sin (2 x) cos (x) : - \infty < x < \infty

Range of

sin (2 x) cos (x) : - \frac{2}{3} sin (2 (- arccos (- \frac{2}{3}) + 2 π)) \leq f (x) \leq \frac{4}{3 3}

Axis interception points of

sin (2 x) cos (x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{π}{2} + 2 πn, 0), (\frac{3 π}{2} + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin (2 x) cos (x) :

None

Extreme Points of

sin (2 x) cos (x) :

Maximum

(arccos (\frac{2}{3}) + 2 πn, \frac{4}{3 3}),

Minimum

(\frac{π}{2} + 2 πn, 0),

Maximum

(arccos (- \frac{2}{3}) + 2 πn, \frac{4}{3 3}),

Minimum

(- arccos (- \frac{2}{3}) + 2 π + 2 πn, - \frac{2}{3} sin (2 (- arccos (- \frac{2}{3}) + 2 π))),

Maximum

(\frac{3 π}{2} + 2 πn, 0),

Minimum

(2 π - arccos (\frac{2}{3}) + 2 πn, \frac{2}{3} sin (2 (2 π - arccos (\frac{2}{3}))))

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Frequently Asked Questions (FAQ)

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