What is the range of (cos(8θ)-cos(4θ))/2 ?

The range of (cos(8θ)-cos(4θ))/2 is -9/16 <= f(θ)<= 1

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range of (cos(8θ)-cos(4θ))/2

range

\frac{cos ( 8 θ ) - cos ( 4 θ )}{2}

- \frac{9}{16} \leq f (θ) \leq 1

Interval Notation

[- \frac{9}{16}, 1]

Solution steps

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

Domain of

\frac{cos ( 8 θ ) - cos ( 4 θ )}{2} : - \infty < θ < \infty

Extreme Points of

\frac{cos ( 8 θ ) - cos ( 4 θ )}{2} :

Maximum

(\frac{π}{2} n, 0),

Minimum

(\frac{arccos ( \frac{1}{4} )}{4} + \frac{π}{2} n, - \frac{9}{16}),

Maximum

(\frac{π}{4} + \frac{π}{2} n, 1),

Minimum

\frac{π}{2} - \frac{arccos ( \frac{1}{4} )}{4} + \frac{π}{2} n, \frac{4 cos ( 8 ( \frac{π}{2} - \frac{a r c c o s ( \frac{1}{4} )}{4} ) ) - 1}{8}

Find the range for the interval

- \infty < θ < \infty : - \frac{9}{16} \leq f (θ) \leq 1

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

- \frac{9}{16} \leq f (θ) \leq 1

2 - 3 cos (2 x)

lo g_{5} (x)

f (x) = - 2 x + 7

f (x) = 2 e^{- 0.7 t}

f (x) = \frac{81 x ^{2} - 18}{3 x - 2}

What is the range of (cos(8θ)-cos(4θ))/2 ?
The range of (cos(8θ)-cos(4θ))/2 is -9/16 <= f(θ)<= 1