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Popular >

f(θ)=1-tan^2(θ)

Solution

f (θ) = 1 - tan^{2} (θ)

Solution

Period : π

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

Range : f (θ) \leq 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 : Maximum (πn, 1)

+1

Interval Notation

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

Range : (- \infty, 1]

Solution steps

Periodicity of

1 - tan^{2} (θ) : π

Domain of

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

Range of

1 - tan^{2} (θ) : f (θ) \leq 1

Axis interception points of

1 - tan^{2} (θ) :

X Intercepts

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

Y Intercepts

: (0, 1)

Asymptotes of

1 - tan^{2} (θ) :

Vertical

: θ = \frac{π}{2} + πn

Extreme Points of

1 - tan^{2} (θ) :

Maximum

(πn, 1)

Popular Examples

f (a) = a - 5

y = - 5 x + 11

y = - 5 x + 32

y = x^{4} - 16

y = x^{4} - 4 x

Frequently Asked Questions (FAQ)

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