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, sin (2 \cdot 0) cos (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, sin (2 \cdot 0) cos (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^'+(xy)/(x^2-1)+1/(x^2-1)=0

y^{^{'}} + \frac{x y}{x ^{2} - 1} + \frac{1}{x ^{2} - 1} = 0

(d^2)/(dx^2)(ln(sqrt(x^2+y^2)))

\frac{d ^{2}}{d x ^{2}} (ln (x^{2} + y^{2}))

integral of (5x^3)/((x-2)(x+3))

\int \frac{5 x ^{3}}{( x - 2 ) ( x + 3 )} d x

(\partial)/(\partial x)(ln(x+z)-yz)

\frac{\partial}{\partial x} (ln (x + z) - yz)

d/(dt)((dx)/(dt))+d/(dt)(6x)+10x=0

\frac{d}{d t} (\frac{d x}{d t}) + \frac{d}{d t} (6 x) + 10 x = 0

Frequently Asked Questions (FAQ)

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