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Popular >

f(θ)=sec(θ)+csc(θ)

Solution

f (θ) = sec (θ) + csc (θ)

Solution

Period : 2 π

Domain : 2 πn < θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < π + 2 πn or π + 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 : (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

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

Extreme Points : Minimum (\frac{π}{4} + 2 πn, 22), Maximum (\frac{5 π}{4} + 2 πn, - 22)

+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, \infty)

Solution steps

Periodicity of

sec (θ) + csc (θ) : 2 π

Domain of

sec (θ) + csc (θ) : 2 πn < θ < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < θ < π + 2 πn or π + 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) + csc (θ) : - \infty < f (θ) < \infty

Axis interception points of

sec (θ) + csc (θ) :

X Intercepts

: (\frac{3 π}{4} + 2 πn, 0), (\frac{7 π}{4} + 2 πn, 0)

Asymptotes of

sec (θ) + csc (θ) :

Vertical

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

Extreme Points of

sec (θ) + csc (θ) :

Minimum

(\frac{π}{4} + 2 πn, 22),

Maximum

(\frac{5 π}{4} + 2 πn, - 22)

Popular Examples

f (θ) = 9 cos (θ)

y = \frac{x + 5}{x - 6}

y= 1/(cot(x)+1)+1/(tan(x)+1)

y = \frac{1}{cot ( x ) + 1} + \frac{1}{tan ( x ) + 1}

y = x^{2} + x + 5

y = x^{2} + x + 6

Frequently Asked Questions (FAQ)

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