Question

For what numbers θ is f(θ) = tan(θ) not defined?

a) θ = nπ, where n is an integer
b) θ = (2n + 1)π/2, where n is an integer
c) θ = nπ/2, where n is an odd integer
d) θ = nπ, where n is an odd integer

Answer 1

The function tan(θ) is not defined when cos(θ) = 0. Therefore, for what numbers θ is f(θ) = tan(θ) not defined? The correct answer is option c) θ = nπ/2, where n is an odd integer.

Step-by-step explanation:

In mathematics, the function tan(θ) is not defined for certain values of θ. Specifically, tan(θ) is not defined when the value of θ makes the denominator of the fraction equal to zero. The denominator of the tan(θ) function is cos(θ). Therefore, when cos(θ) = 0, the function is not defined.

Using this information, we can determine that the correct answer is option c) θ = nπ/2, where n is an odd integer. This is because for odd values of n, cos(nπ/2) = 0, making tan(nπ/2) undefined.

For example, when n = 1, θ = π/2, and tan(π/2) is undefined.

The function f(θ) = tan(θ) is not defined for angles θ at which the value of the cosine function is zero, because the tangent function is the ratio of the sine function to the cosine function, and division by zero is undefined.