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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

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}

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Frequently Asked Questions (FAQ)

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