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Popular >

f(θ)=sec(θ)tan(θ)

Solution

f (θ) = sec (θ) tan (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 : - \infty < f (θ) < \infty

X Intercepts : (2 πn, 0), (π + 2 πn, 0), Y Intercepts : (0, 0)

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

Extreme Points : None

+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, \infty)

Solution steps

Periodicity of

sec (θ) tan (θ) : 2 π

Domain of

sec (θ) tan (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) tan (θ) : - \infty < f (θ) < \infty

Axis interception points of

sec (θ) tan (θ) :

X Intercepts

: (2 πn, 0), (π + 2 πn, 0),

Y Intercepts

: (0, 0)

Asymptotes of

sec (θ) tan (θ) :

Vertical

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

Extreme Points of

sec (θ) tan (θ) :

None

Popular Examples

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\int_{1}^{2} x^{2} + 1 d x

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\int e^{c x} d x

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x \to 0 + lim (\frac{3}{x} - \frac{3}{∣ x ∣})

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y = x^{3} - 3 x + 2

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\int \frac{sec ^{4} ( t )}{tan ^{3} ( t )} d t

Frequently Asked Questions (FAQ)

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