Question

What is the maximum value of tan theta? I need full explanation​

Answer 1

Answer:

tan θ does not have any maximum or minimum values. tan θ = 1 when θ = 45 ˚ and 225˚ . the maximum value of tan theta is infinity. tan θ does not have any maximum or minimum values.

Answer 2

EXPLANATION.

Maximum value of tanθ.

As we know that,

Let we take a function.

⇒ y = tan(x).

Put the value of x = - π/2 in the equation, we get.

⇒ y = tan(-π/2).

⇒ y = - ∞.

Put the value of x = 0 in the equation, we get.

⇒ y = tan(0).

⇒ y = 0.

Put the value of x = + π/2 in the equation, we get.

⇒ y = tan(π/2).

⇒ y = + ∞.

Plot this point on the graph, we get.

After plotting this point, we get.

⇒ Domain = R - (2n + 1)π/2, n ∈ I.

⇒ Range = R = (- ∞, + ∞).

It is discontinuous function at x = (2n + 1)π/2, n ∈ I.

It is a periodic function.

Period = π.

Maximum value of tanθ = + ∞.