en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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}))))

Popular Examples

y = - x^{2} - 14 x - 42

f(x)=log_{2}(-x)

f (x) = lo g_{2} (- x)

f (t) = t e^{2 t}

f (x) = \frac{2}{x + 4}

y = 2^{x - 3}

Frequently Asked Questions (FAQ)

What is the f(x)=sin(2x)cos(x) ?
The f(x)=sin(2x)cos(x) is