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Popular Calculus >

f(θ)=sec(θ)

Solution

f (θ) = sec (θ)

Solution

Period : 2 π

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

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

Y Intercepts : (0, 1)

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

Domain of

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

Range of

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

Axis interception points of

sec (θ) :

Y Intercepts

: (0, 1)

Asymptotes of

sec (θ) :

Vertical

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

Extreme Points of

sec (θ) :

Minimum

(2 πn, 1),

Maximum

(π + 2 πn, - 1)

Graph

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