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Popular >

f(x)=(cos(x))/(sec^2(x))

Solution

f (x) = \frac{cos ( x )}{sec ^{2} ( x )}

Solution

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

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

Y Intercepts : (0, 1)

Asymptotes : None

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

+1

Interval Notation

Domain : [2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Range : [- 1, 1]

Solution steps

Periodicity of

\frac{cos ( x )}{sec ^{2} ( x )} : 2 π

Domain of

\frac{cos ( x )}{sec ^{2} ( x )} : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range of

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

Axis interception points of

\frac{cos ( x )}{sec ^{2} ( x )} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{cos ( x )}{sec ^{2} ( x )} :

None

Extreme Points of

\frac{cos ( x )}{sec ^{2} ( x )} :

Maximum

(2 πn, 1),

Minimum

(π + 2 πn, - 1)

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Frequently Asked Questions (FAQ)

What is the f(x)=(cos(x))/(sec^2(x)) ?
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