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Popular >

f(θ)=tan^2(θ)-1

Solution

f (θ) = tan^{2} (θ) - 1

Solution

Period : π

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

Range : f (θ) \geq - 1

X Intercepts : (\frac{π}{4} + πn, 0), (\frac{3 π}{4} + πn, 0), Y Intercepts : (0, - 1)

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

Extreme Points : Minimum (πn, - 1)

+1

Interval Notation

Domain : [πn, \frac{π}{2} + πn) \cup (\frac{π}{2} + πn, π + πn)

Range : [- 1, \infty)

Solution steps

Periodicity of

tan^{2} (θ) - 1 : π

Domain of

tan^{2} (θ) - 1 : πn \leq θ < \frac{π}{2} + πn or \frac{π}{2} + πn < θ < π + πn

Range of

tan^{2} (θ) - 1 : f (θ) \geq - 1

Axis interception points of

tan^{2} (θ) - 1 :

X Intercepts

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

Y Intercepts

: (0, - 1)

Asymptotes of

tan^{2} (θ) - 1 :

Vertical

: θ = \frac{π}{2} + πn

Extreme Points of

tan^{2} (θ) - 1 :

Minimum

(πn, - 1)

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Frequently Asked Questions (FAQ)

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