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Popular >

f(t)=sec(t)

Solution

f (t) = sec (t)

Solution

Period : 2 π

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

Range : f (t) \leq - 1 or f (t) \geq 1

Y Intercepts : (0, 1)

Asymptotes : Vertical t = \frac{3 π}{2} + 2 πn, t = \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 (t) : 2 π

Domain of

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

Range of

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

Axis interception points of

sec (t) :

Y Intercepts

: (0, 1)

Asymptotes of

sec (t) :

Vertical

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

Extreme Points of

sec (t) :

Minimum

(2 πn, 1),

Maximum

(π + 2 πn, - 1)

Popular Examples

sum from n=0 to infinity of (e/(6pi))^n

n = 0 \sum \infty (\frac{e}{6 π})^{n}

partialfraction (x^2)/(1-x)partial fractions

\frac{x ^{2}}{1 - x}

y^{''}+3y^'-10y=6e^{4x}

y^{^{''}} + 3 y^{^{'}} - 10 y = 6 e^{4 x}

integral from 0 to 2 of 1/(sqrt(16+x^2))

\int_{0}^{2} \frac{1}{16 + x ^{2}} d x

integral of x/(sqrt(x-9))

\int \frac{x}{x - 9} d x

Frequently Asked Questions (FAQ)

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