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

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{2 π}{3} + 2 πn, 0), (\frac{4 π}{3} + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

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

Axis interception points of

- sin (2 x) - sin (x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{2 π}{3} + 2 πn, 0), (\frac{4 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) :

Minimum

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

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

Maximum

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

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Frequently Asked Questions (FAQ)

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