What is the range of (cos(x))/(2+sin(x)) ?

The range of (cos(x))/(2+sin(x)) is -1/(sqrt(3))<= f(x)<= 1/(sqrt(3))

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range of (cos(x))/(2+sin(x))

range

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

- \frac{1}{3} \leq f (x) \leq \frac{1}{3}

Interval Notation

[- \frac{1}{3}, \frac{1}{3}]

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

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

Extreme Points of

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

Minimum

(\frac{7 π}{6} + 2 πn, - \frac{1}{3}),

Maximum

(\frac{11 π}{6} + 2 πn, \frac{1}{3})

Find the range for the interval

- \infty < x < \infty : - \frac{1}{3} \leq f (x) \leq \frac{1}{3}

Combine the ranges of all domain intervals to obtain the function range

- \frac{1}{3} \leq f (x) \leq \frac{1}{3}

f (x) = \frac{x + 4}{4}

\frac{2 x + 1}{3}

\frac{1}{2 x + 4}

f (x) = x^{2} + 6 x + 8

f (x) = \frac{( 2 e ^{x} )}{e ^{x} - 6}

What is the range of (cos(x))/(2+sin(x)) ?
The range of (cos(x))/(2+sin(x)) is -1/(sqrt(3))<= f(x)<= 1/(sqrt(3))