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Popular >

f(x)=(sin(x))/(1+2cos(x))

Solution

f (x) = \frac{sin ( x )}{1 + 2 cos ( x )}

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{2 π}{3} + 2 πn or \frac{2 π}{3} + 2 πn < x < \frac{4 π}{3} + 2 πn or \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

Range : - \infty < f (x) < \infty

X Intercepts : (2 πn, 0), (π + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Extreme Points : None

+1

Interval Notation

Domain : [2 πn, \frac{2 π}{3} + 2 πn) \cup (\frac{2 π}{3} + 2 πn, \frac{4 π}{3} + 2 πn) \cup (\frac{4 π}{3} + 2 πn, 2 π + 2 πn)

Range : (- \infty, \infty)

Solution steps

Periodicity of

\frac{sin ( x )}{1 + 2 cos ( x )} : 2 π

Domain of

\frac{sin ( x )}{1 + 2 cos ( x )} : 2 πn \leq x < \frac{2 π}{3} + 2 πn or \frac{2 π}{3} + 2 πn < x < \frac{4 π}{3} + 2 πn or \frac{4 π}{3} + 2 πn < x < 2 π + 2 πn

Range of

\frac{sin ( x )}{1 + 2 cos ( x )} : - \infty < f (x) < \infty

Axis interception points of

\frac{sin ( x )}{1 + 2 cos ( x )} :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

\frac{sin ( x )}{1 + 2 cos ( x )} :

Vertical

: x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Extreme Points of

\frac{sin ( x )}{1 + 2 cos ( x )} :

None

Popular Examples

y^{^{'}} = y - 2

(\partial)/(\partial x)(xln(z^7+x^3))

\frac{\partial}{\partial x} (x ln (z^{7} + x^{3}))

derivative of y= 1/(2sqrt(x-2))derivative of

y = \frac{1}{2 x - 2}

limit as x approaches 7 of (2x+1)/(x-7)

x \to 7 lim (\frac{2 x + 1}{x - 7})

integral of 2cos(5x)

\int 2 cos (5 x) d x

Frequently Asked Questions (FAQ)

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