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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

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

X Intercepts : (\frac{π}{4} + 2 πn, 0), (\frac{7 π}{12} + 2 πn, 0), (\frac{11 π}{12} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), (\frac{19 π}{12} + 2 πn, 0), (\frac{23 π}{12} + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (\frac{π}{12} + 2 πn, 2), Minimum (\frac{5 π}{12} + 2 πn, - 2), Maximum (\frac{3 π}{4} + 2 πn, 2), Minimum (\frac{13 π}{12} + 2 πn, - 2), Maximum (\frac{17 π}{12} + 2 πn, 2), Minimum (\frac{7 π}{4} + 2 πn, - 2)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 2, 2]

Solution steps

Periodicity of

cos (3 x) + sin (3 x) : 2 π

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

: (\frac{π}{4} + 2 πn, 0), (\frac{7 π}{12} + 2 πn, 0), (\frac{11 π}{12} + 2 πn, 0), (\frac{5 π}{4} + 2 πn, 0), (\frac{19 π}{12} + 2 πn, 0), (\frac{23 π}{12} + 2 πn, 0),

Y Intercepts

: (0, 1)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(\frac{π}{12} + 2 πn, 2),

Minimum

(\frac{5 π}{12} + 2 πn, - 2),

Maximum

(\frac{3 π}{4} + 2 πn, 2),

Minimum

(\frac{13 π}{12} + 2 πn, - 2),

Maximum

(\frac{17 π}{12} + 2 πn, 2),

Minimum

(\frac{7 π}{4} + 2 πn, - 2)

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Frequently Asked Questions (FAQ)

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