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Popular >

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

Solution

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

Solution

Period : π

Domain : - \infty < x < \infty

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

Asymptotes : None

Inflection Points : (πn, 0), (arcsin (\frac{3}{4}) + πn, \frac{9 7}{64}), (\frac{π}{2} + πn, 0), (π - arcsin (\frac{3}{4}) + πn, - \frac{7}{4} sin (3 (π - arcsin (\frac{3}{4})))), (- arcsin (\frac{3}{4}) + π + πn, - \frac{7}{4} sin (3 (- arcsin (\frac{3}{4}) + π)))

+1

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Periodicity of

sin (3 x) cos (x) : π

Domain of

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

Axis interception points of

sin (3 x) cos (x) :

X Intercepts

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

Y Intercepts

: (0, sin (3 \cdot 0) cos (0))

Asymptotes of

sin (3 x) cos (x) :

None

Inflection Points of

sin (3 x) cos (x) : (πn, 0), (arcsin (\frac{3}{4}) + πn, \frac{9 7}{64}), (\frac{π}{2} + πn, 0), (π - arcsin (\frac{3}{4}) + πn, - \frac{7}{4} sin (3 (π - arcsin (\frac{3}{4})))), (- arcsin (\frac{3}{4}) + π + πn, - \frac{7}{4} sin (3 (- arcsin (\frac{3}{4}) + π)))

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f(x)=-16t^2+128t

f (x) = - 16 t^{2} + 128 t

Frequently Asked Questions (FAQ)

What is the f(x)=sin(3x)cos(x) ?
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