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Popular >

y=sec(x)

Solution

y = 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 : f (x) \leq - 1 or f (x) \geq 1

Y Intercepts : (0, 1)

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

Extreme Points : Minimum (2 πn, 1), Maximum (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 : (- \infty, - 1] \cup [1, \infty)

Solution steps

Periodicity of

sec (x) : 2 π

Domain of

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

sec (x) : f (x) \leq - 1 or f (x) \geq 1

Axis interception points of

sec (x) :

Y Intercepts

: (0, 1)

Asymptotes of

sec (x) :

Vertical

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

Extreme Points of

sec (x) :

Minimum

(2 πn, 1),

Maximum

(π + 2 πn, - 1)

Popular Examples

inverse of f(x)= 4/(x+1)+3 inverse

f (x) = \frac{4}{x + 1} + 3

inverse of sqrt(x)-4 inverse

x - 4

range of f(x)=e^{t^2}-4 range

f (x) = e^{t^{2}} - 4

extreme f(x)=(3x^2)/(x^2-4)extreme points

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

distance (0,0),(8,6)distance

(0, 0), (8, 6)

Frequently Asked Questions (FAQ)

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