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Popular >

f(t)=3cos(2t)+4sin(2t)

Solution

f (t) = 3 cos (2 t) + 4 sin (2 t)

Solution

Period : π

Domain : - \infty < t < \infty

Range : - 5 \leq f (t) \leq 5

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

Asymptotes : None

Extreme Points : Maximum (\frac{arctan ( \frac{4}{3} )}{2} + πn, 5), Minimum (\frac{arctan ( \frac{4}{3} ) + π}{2} + πn, - 5)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 5, 5]

Solution steps

Periodicity of

3 cos (2 t) + 4 sin (2 t) : π

Domain of

3 cos (2 t) + 4 sin (2 t) : - \infty < t < \infty

Range of

3 cos (2 t) + 4 sin (2 t) : - 5 \leq f (t) \leq 5

Axis interception points of

3 cos (2 t) + 4 sin (2 t) :

X Intercepts

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

Y Intercepts

: (0, 3)

Asymptotes of

3 cos (2 t) + 4 sin (2 t) :

None

Extreme Points of

3 cos (2 t) + 4 sin (2 t) :

Maximum

(\frac{arctan ( \frac{4}{3} )}{2} + πn, 5),

Minimum

(\frac{arctan ( \frac{4}{3} ) + π}{2} + πn, - 5)

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Frequently Asked Questions (FAQ)

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