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Popular >

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

Solution

f (t) = \frac{1 + cos ( t )}{1 + sec ( 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 : - 1 < f (t) \leq 1

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (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 : (- 1, 1]

Solution steps

Periodicity of

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

Domain of

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

Axis interception points of

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

Y Intercepts

: (0, 1)

Asymptotes of

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

None

Extreme Points of

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

Maximum

(2 πn, 1)

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Frequently Asked Questions (FAQ)

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