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Popular >

f(t)=sin(t)cos(2t)

Solution

f (t) = sin (t) cos (2 t)

Solution

Period : 2 π

Domain : - \infty < t < \infty

Range : - 1 \leq f (t) \leq 1

X Intercepts : (2 πn, 0), (π + 2 πn, 0), (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0), Y Intercepts : (0, sin (0) cos (2 \cdot 0))

Asymptotes : None

Extreme Points : Maximum (arccos (\frac{5}{6}) + 2 πn, \frac{2}{3 3}), Minimum (\frac{π}{2} + 2 πn, - 1), Maximum (arccos (- \frac{5}{6}) + 2 πn, \frac{2}{3 3}), Minimum (- arccos (- \frac{5}{6}) + 2 π + 2 πn, - \frac{1}{6} cos (2 (- arccos (- \frac{5}{6}) + 2 π))), Maximum (\frac{3 π}{2} + 2 πn, 1), Minimum (2 π - arccos (\frac{5}{6}) + 2 πn, - \frac{1}{6} cos (2 (2 π - arccos (\frac{5}{6}))))

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

sin (t) cos (2 t) : 2 π

Domain of

sin (t) cos (2 t) : - \infty < t < \infty

Range of

sin (t) cos (2 t) : - 1 \leq f (t) \leq 1

Axis interception points of

sin (t) cos (2 t) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0), (\frac{π}{4} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0),

Y Intercepts

: (0, sin (0) cos (2 \cdot 0))

Asymptotes of

sin (t) cos (2 t) :

None

Extreme Points of

sin (t) cos (2 t) :

Maximum

(arccos (\frac{5}{6}) + 2 πn, \frac{2}{3 3}),

Minimum

(\frac{π}{2} + 2 πn, - 1),

Maximum

(arccos (- \frac{5}{6}) + 2 πn, \frac{2}{3 3}),

Minimum

(- arccos (- \frac{5}{6}) + 2 π + 2 πn, - \frac{1}{6} cos (2 (- arccos (- \frac{5}{6}) + 2 π))),

Maximum

(\frac{3 π}{2} + 2 πn, 1),

Minimum

(2 π - arccos (\frac{5}{6}) + 2 πn, - \frac{1}{6} cos (2 (2 π - arccos (\frac{5}{6}))))

Popular Examples

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f (x) = (x + 7) (x - 1)

Frequently Asked Questions (FAQ)

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