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Popular >

y=2sin(x)+cos(2x)

Solution

y = 2 sin (x) + cos (2 x)

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 3 \leq f (x) \leq \frac{3}{2}

X Intercepts : (- arcsin (\frac{3 - 1}{2}) + 2 π + 2 πn, 0), (π + arcsin (\frac{- 1 + 3}{2}) + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 3, \frac{3}{2}]

Solution steps

Periodicity of

2 sin (x) + cos (2 x) : 2 π

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

: (- arcsin (\frac{3 - 1}{2}) + 2 π + 2 πn, 0), (π + arcsin (\frac{- 1 + 3}{2}) + 2 πn, 0),

Y Intercepts

: (0, 1)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(\frac{π}{6} + 2 πn, \frac{3}{2}),

Minimum

(\frac{π}{2} + 2 πn, 1),

Maximum

(\frac{5 π}{6} + 2 πn, \frac{3}{2}),

Minimum

(\frac{3 π}{2} + 2 πn, - 3)

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Frequently Asked Questions (FAQ)

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