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Popular Functions >

f(t)=(1+sec(t))/(1+cos(t))

Solution

f (t) = \frac{1 + sec ( t )}{1 + cos ( t )}

Solution

Period : 2 π

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

Range : f (t) < - 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)

+1

Interval Notation

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

\frac{1 + sec ( t )}{1 + cos ( t )} : 2 π

Domain of

\frac{1 + sec ( t )}{1 + cos ( t )} : 2 πn \leq t < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < t < π + 2 πn or π + 2 πn < t < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < t < 2 π + 2 πn

Range of

\frac{1 + sec ( t )}{1 + cos ( t )} : f (t) < - 1 or f (t) \geq 1

Axis interception points of

\frac{1 + sec ( t )}{1 + cos ( t )} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{1 + sec ( t )}{1 + cos ( t )} :

Vertical

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

Extreme Points of

\frac{1 + sec ( t )}{1 + cos ( t )} :

Minimum

(2 πn, 1)

Graph

Popular Examples

Frequently Asked Questions (FAQ)

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