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Popular >

f(θ)=3sec(θ)

Solution

f (θ) = 3 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 - 3 or f (θ) \geq 3

Y Intercepts : (0, 3)

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

Extreme Points : Minimum (2 πn, 3), Maximum (π + 2 πn, - 3)

+1

Solution steps

Periodicity of

3 sec (θ) : 2 π

Domain of

3 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

3 sec (θ) : f (θ) \leq - 3 or f (θ) \geq 3

Axis interception points of

3 sec (θ) :

Y Intercepts

: (0, 3)

Asymptotes of

3 sec (θ) :

Vertical

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

Extreme Points of

3 sec (θ) :

Minimum

(2 πn, 3),

Maximum

(π + 2 πn, - 3)

Popular Examples

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\int \frac{( x ^{2} + 3 x - 1 )}{x} d x

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(5, 6), (3, 4)

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\int_{0}^{9} π y d y

integral of 2x(1+2x)^4

\int 2 x (1 + 2 x)^{4} d x

laplacetransform 1-e^{-2t}laplace transform

1 - e^{- 2 t}

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