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Popular >

f(θ)=cos(2θ)+cos(4θ)

Solution

f (θ) = cos (2 θ) + cos (4 θ)

Solution

Period : π

Domain : - \infty < θ < \infty

Range : - \frac{9}{8} \leq f (θ) \leq 2

X Intercepts : (\frac{π}{6} + πn, 0), (\frac{5 π}{6} + πn, 0), (\frac{π}{2} + πn, 0), Y Intercepts : (0, 2)

Asymptotes : None

Extreme Points : Maximum (πn, 2), Minimum (\frac{arccos ( - \frac{1}{4} )}{2} + πn, - \frac{9}{8}), Maximum (\frac{π}{2} + πn, 0), Minimum (\frac{- arccos ( - \frac{1}{4} ) + 2 π}{2} + πn, - \frac{1}{4} + cos (4 (- \frac{arccos ( - \frac{1}{4} )}{2} + π)))

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Solution steps

Periodicity of

cos (2 θ) + cos (4 θ) : π

Domain of

cos (2 θ) + cos (4 θ) : - \infty < θ < \infty

Range of

cos (2 θ) + cos (4 θ) : - \frac{9}{8} \leq f (θ) \leq 2

Axis interception points of

cos (2 θ) + cos (4 θ) :

X Intercepts

: (\frac{π}{6} + πn, 0), (\frac{5 π}{6} + πn, 0), (\frac{π}{2} + πn, 0),

Y Intercepts

: (0, 2)

Asymptotes of

cos (2 θ) + cos (4 θ) :

None

Extreme Points of

cos (2 θ) + cos (4 θ) :

Maximum

(πn, 2),

Minimum

(\frac{arccos ( - \frac{1}{4} )}{2} + πn, - \frac{9}{8}),

Maximum

(\frac{π}{2} + πn, 0),

Minimum

(\frac{- arccos ( - \frac{1}{4} ) + 2 π}{2} + πn, - \frac{1}{4} + cos (4 (- \frac{arccos ( - \frac{1}{4} )}{2} + π)))

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Frequently Asked Questions (FAQ)

What is the f(θ)=cos(2θ)+cos(4θ) ?
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