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Popular Functions >

f(x)=sin(x)+cos(2x)+sec(3x)

Solution

f (x) = sin (x) + cos (2 x) + sec (3 x)

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{6} + 2 πn or \frac{π}{6} + 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{5 π}{6} + 2 πn or \frac{5 π}{6} + 2 πn < x < \frac{7 π}{6} + 2 πn or \frac{7 π}{6} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < \frac{11 π}{6} + 2 πn or \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

Y Intercepts : (0, 2)

Asymptotes : Vertical x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn

+1

Interval Notation

Domain : [2 πn, \frac{π}{6} + 2 πn) \cup (\frac{π}{6} + 2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{5 π}{6} + 2 πn) \cup (\frac{5 π}{6} + 2 πn, \frac{7 π}{6} + 2 πn) \cup (\frac{7 π}{6} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, \frac{11 π}{6} + 2 πn) \cup (\frac{11 π}{6} + 2 πn, 2 π + 2 πn)

Solution steps

Periodicity of

sin (x) + cos (2 x) + sec (3 x) : 2 π

Domain of

sin (x) + cos (2 x) + sec (3 x) : 2 πn \leq x < \frac{π}{6} + 2 πn or \frac{π}{6} + 2 πn < x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{5 π}{6} + 2 πn or \frac{5 π}{6} + 2 πn < x < \frac{7 π}{6} + 2 πn or \frac{7 π}{6} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < \frac{11 π}{6} + 2 πn or \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

Axis interception points of

sin (x) + cos (2 x) + sec (3 x) :

Y Intercepts

: (0, 2)

Asymptotes of

sin (x) + cos (2 x) + sec (3 x) :

Vertical

: x = \frac{11 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn, x = \frac{π}{6} + 2 πn

Graph

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Frequently Asked Questions (FAQ)

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