en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

f(θ)=cos^4(θ)+sin^4(θ)

Solution

f (θ) = cos^{4} (θ) + sin^{4} (θ)

Solution

Period : π

Domain : - \infty < θ < \infty

Range : \frac{1}{2} \leq f (θ) \leq 1

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (πn, 1), Minimum (\frac{π}{4} + πn, \frac{1}{2}), Maximum (\frac{π}{2} + πn, 1), Minimum (\frac{3 π}{4} + πn, \frac{1}{2})

+1

Interval Notation

Domain : (- \infty, \infty)

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

Solution steps

Periodicity of

cos^{4} (θ) + sin^{4} (θ) : π

Domain of

cos^{4} (θ) + sin^{4} (θ) : - \infty < θ < \infty

Range of

cos^{4} (θ) + sin^{4} (θ) : \frac{1}{2} \leq f (θ) \leq 1

Axis interception points of

cos^{4} (θ) + sin^{4} (θ) :

Y Intercepts

: (0, 1)

Asymptotes of

cos^{4} (θ) + sin^{4} (θ) :

None

Extreme Points of

cos^{4} (θ) + sin^{4} (θ) :

Maximum

(πn, 1),

Minimum

(\frac{π}{4} + πn, \frac{1}{2}),

Maximum

(\frac{π}{2} + πn, 1),

Minimum

(\frac{3 π}{4} + πn, \frac{1}{2})

Popular Examples

y = \frac{x + 3}{2}

f(θ)=cos^2(θ/2)

f (θ) = cos^{2} (\frac{θ}{2})

y = x^{4} - 6 x^{2}

f(x)=(3x^2+15x)/(5x^2)

f (x) = \frac{3 x ^{2} + 15 x}{5 x ^{2}}

f(x)=2(x-3)^2+4

f (x) = 2 (x - 3)^{2} + 4

Frequently Asked Questions (FAQ)

What is the f(θ)=cos^4(θ)+sin^4(θ) ?
The f(θ)=cos^4(θ)+sin^4(θ) is