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Popular Functions >

f(x)=cos^4(x/2)-sin^4(x/2)

Solution

f (x) = cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2})

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq 1

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

Asymptotes : None

Extreme Points : Maximum (2 πn, 1), Minimum (π + 2 πn, - 1)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, 1]

Solution steps

Periodicity of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}) : 2 π

Domain of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}) : - \infty < x < \infty

Range of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}) : - 1 \leq f (x) \leq 1

Axis interception points of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}) :

X Intercepts

: (\frac{3 π}{2} + 2 πn, 0), (\frac{π}{2} + 2 πn, 0),

Y Intercepts

: (0, 1)

Asymptotes of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}) :

None

Extreme Points of

cos^{4} (\frac{x}{2}) - sin^{4} (\frac{x}{2}) :

Maximum

(2 πn, 1),

Minimum

(π + 2 πn, - 1)

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=cos^4(x/2)-sin^4(x/2) ?
The f(x)=cos^4(x/2)-sin^4(x/2) is