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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

Range : - 1 \leq f (x) \leq \frac{5}{4}

X Intercepts : (arcsin (\frac{5 - 1}{2}) + 2 πn, 0), (π - arcsin (\frac{5 - 1}{2}) + 2 πn, 0), Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Minimum (\frac{π}{2} + 2 πn, - 1), Maximum (\frac{7 π}{6} + 2 πn, \frac{5}{4}), Minimum (\frac{3 π}{2} + 2 πn, 1), Maximum (\frac{11 π}{6} + 2 πn, \frac{5}{4})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- 1, \frac{5}{4}]

Solution steps

Periodicity of

cos^{2} (x) - sin (x) : 2 π

Domain of

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

Range of

cos^{2} (x) - sin (x) : - 1 \leq f (x) \leq \frac{5}{4}

Axis interception points of

cos^{2} (x) - sin (x) :

X Intercepts

: (arcsin (\frac{5 - 1}{2}) + 2 πn, 0), (π - arcsin (\frac{5 - 1}{2}) + 2 πn, 0),

Y Intercepts

: (0, 1)

Asymptotes of

cos^{2} (x) - sin (x) :

None

Extreme Points of

cos^{2} (x) - sin (x) :

Minimum

(\frac{π}{2} + 2 πn, - 1),

Maximum

(\frac{7 π}{6} + 2 πn, \frac{5}{4}),

Minimum

(\frac{3 π}{2} + 2 πn, 1),

Maximum

(\frac{11 π}{6} + 2 πn, \frac{5}{4})

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Frequently Asked Questions (FAQ)

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