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Popular >

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

Solution

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

Solution

Period : 2 π

Domain : - \infty < x < \infty

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

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

Asymptotes : None

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

+1

Interval Notation

Domain : (- \infty, \infty)

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

Solution steps

Periodicity of

- sin (x) - cos^{2} (x) : 2 π

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

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

Y Intercepts

: (0, - 1)

Asymptotes of

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

None

Extreme Points of

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

Minimum

(\frac{π}{6} + 2 πn, - \frac{5}{4}),

Maximum

(\frac{π}{2} + 2 πn, - 1),

Minimum

(\frac{5 π}{6} + 2 πn, - \frac{5}{4}),

Maximum

(\frac{3 π}{2} + 2 πn, 1)

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Frequently Asked Questions (FAQ)

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