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Popular >

f(θ)=(cos(2θ))/2

Solution

f (θ) = \frac{cos ( 2 θ )}{2}

Solution

Period : π

Domain : - \infty < θ < \infty

Range : - \frac{1}{2} \leq f (θ) \leq \frac{1}{2}

X Intercepts : (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0), Y Intercepts : (0, \frac{1}{2})

Asymptotes : None

Extreme Points : Maximum (πn, \frac{1}{2}), Minimum (\frac{π}{2} + πn, - \frac{1}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{2}, \frac{1}{2}]

Solution steps

Periodicity of

\frac{cos ( 2 θ )}{2} : π

Domain of

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

Range of

\frac{cos ( 2 θ )}{2} : - \frac{1}{2} \leq f (θ) \leq \frac{1}{2}

Axis interception points of

\frac{cos ( 2 θ )}{2} :

X Intercepts

: (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0),

Y Intercepts

: (0, \frac{1}{2})

Asymptotes of

\frac{cos ( 2 θ )}{2} :

None

Extreme Points of

\frac{cos ( 2 θ )}{2} :

Maximum

(πn, \frac{1}{2}),

Minimum

(\frac{π}{2} + πn, - \frac{1}{2})

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Frequently Asked Questions (FAQ)

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