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)-sin(x)

Solution

f (x) = sin (2 x) - sin (x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : sin (2 arccos (\frac{1 - 33}{8})) - 1 - \frac{17 - 33}{32} \leq f (x) \leq sin (2 (- arccos (\frac{1 - 33}{8}) + 2 π)) + 1 - \frac{17 - 33}{32}

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

Extreme Points : Maximum arccos (\frac{1 + 33}{8}) + 2 πn, sin (2 arccos (\frac{1 + 33}{8})) - 1 - \frac{17 + 33}{32}, Minimum arccos (\frac{1 - 33}{8}) + 2 πn, sin (2 arccos (\frac{1 - 33}{8})) - 1 - \frac{17 - 33}{32}, Maximum - arccos (\frac{1 - 33}{8}) + 2 π + 2 πn, sin (2 (- arccos (\frac{1 - 33}{8}) + 2 π)) + 1 - \frac{17 - 33}{32}, Minimum 2 π - arccos (\frac{1 + 33}{8}) + 2 πn, sin (2 (2 π - arccos (\frac{1 + 33}{8}))) + 1 - \frac{17 + 33}{32}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : sin (2 arccos (\frac{1 - 33}{8})) - 1 - \frac{17 - 33}{32}, sin (2 (- arccos (\frac{1 - 33}{8}) + 2 π)) + 1 - \frac{17 - 33}{32}

Solution steps

Periodicity of

sin (2 x) - sin (x) : 2 π

Domain of

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

Range of

sin (2 x) - sin (x) : sin (2 arccos (\frac{1 - 33}{8})) - 1 - \frac{17 - 33}{32} \leq f (x) \leq sin (2 (- arccos (\frac{1 - 33}{8}) + 2 π)) + 1 - \frac{17 - 33}{32}

Axis interception points of

sin (2 x) - sin (x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{π}{3} + 2 πn, 0), (\frac{5 π}{3} + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sin (2 x) - sin (x) :

None

Extreme Points of

sin (2 x) - sin (x) :

Maximum

arccos (\frac{1 + 33}{8}) + 2 πn, sin (2 arccos (\frac{1 + 33}{8})) - 1 - \frac{17 + 33}{32},

Minimum

arccos (\frac{1 - 33}{8}) + 2 πn, sin (2 arccos (\frac{1 - 33}{8})) - 1 - \frac{17 - 33}{32},

Maximum

- arccos (\frac{1 - 33}{8}) + 2 π + 2 πn, sin (2 (- arccos (\frac{1 - 33}{8}) + 2 π)) + 1 - \frac{17 - 33}{32},

Minimum

2 π - arccos (\frac{1 + 33}{8}) + 2 πn, sin (2 (2 π - arccos (\frac{1 + 33}{8}))) + 1 - \frac{17 + 33}{32}

Popular Examples

f (x) = ln^{3} (x)

y = x cos (x)

y = x^{2} + 4 x - 1

f (s) = s^{2}

f (x) = x^{2} + 4 x + 20

Frequently Asked Questions (FAQ)

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