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Popular >

f(x)=sin(3x)+cos(2x)sin(x)

Solution

f (x) = sin (3 x) + cos (2 x) sin (x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 2 \leq f (x) \leq 2

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

Asymptotes : None

Extreme Points : Maximum (arccos (\frac{7}{3}) + 2 πn, 2 - \frac{2}{9}), Minimum (\frac{π}{2} + 2 πn, - 2), Maximum (arccos (- \frac{7}{3}) + 2 πn, 2 - \frac{2}{9}), Minimum (- arccos (- \frac{7}{3}) + 2 π + 2 πn, sin (3 (- arccos (- \frac{7}{3}) + 2 π)) - \frac{2}{3} cos (2 (- arccos (- \frac{7}{3}) + 2 π))), Maximum (\frac{3 π}{2} + 2 πn, 2), Minimum (2 π - arccos (\frac{7}{3}) + 2 πn, sin (3 (2 π - arccos (\frac{7}{3}))) - \frac{2}{3} cos (2 (2 π - arccos (\frac{7}{3}))))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 2, 2]

Solution steps

Periodicity of

sin (3 x) + cos (2 x) sin (x) : 2 π

Domain of

sin (3 x) + cos (2 x) sin (x) : - \infty < x < \infty

Range of

sin (3 x) + cos (2 x) sin (x) : - 2 \leq f (x) \leq 2

Axis interception points of

sin (3 x) + cos (2 x) sin (x) :

X Intercepts

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

Y Intercepts

: (0, 0)

Asymptotes of

sin (3 x) + cos (2 x) sin (x) :

None

Extreme Points of

sin (3 x) + cos (2 x) sin (x) :

Maximum

(arccos (\frac{7}{3}) + 2 πn, 2 - \frac{2}{9}),

Minimum

(\frac{π}{2} + 2 πn, - 2),

Maximum

(arccos (- \frac{7}{3}) + 2 πn, 2 - \frac{2}{9}),

Minimum

(- arccos (- \frac{7}{3}) + 2 π + 2 πn, sin (3 (- arccos (- \frac{7}{3}) + 2 π)) - \frac{2}{3} cos (2 (- arccos (- \frac{7}{3}) + 2 π))),

Maximum

(\frac{3 π}{2} + 2 πn, 2),

Minimum

(2 π - arccos (\frac{7}{3}) + 2 πn, sin (3 (2 π - arccos (\frac{7}{3}))) - \frac{2}{3} cos (2 (2 π - arccos (\frac{7}{3}))))

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Frequently Asked Questions (FAQ)

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