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Popular >

f(x)=tan^2(x)sec(x)

Solution

f (x) = tan^{2} (x) sec (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 : - \infty < f (x) < \infty

X Intercepts : (2 πn, 0), (π + 2 πn, 0), Y Intercepts : (0, 0)

Asymptotes : Vertical x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Extreme Points : Minimum (2 πn, 0), Maximum (π + 2 πn, 0)

+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 : (- \infty, \infty)

Solution steps

Periodicity of

tan^{2} (x) sec (x) : 2 π

Domain of

tan^{2} (x) sec (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

tan^{2} (x) sec (x) : - \infty < f (x) < \infty

Axis interception points of

tan^{2} (x) sec (x) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

tan^{2} (x) sec (x) :

Vertical

: x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Extreme Points of

tan^{2} (x) sec (x) :

Minimum

(2 πn, 0),

Maximum

(π + 2 πn, 0)

Popular Examples

y = - 2 x^{2} - 4 x - 3

y = - x^{2} - 3 x + 18

f (x) = 48 x^{2}

f(x)=6x+arctan(9x)

f (x) = 6 x + arctan (9 x)

y = x + 2 [1.5]

Frequently Asked Questions (FAQ)

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