Question Video: Finding the Values Where the Tangent Function Is Undefined | Nagwa Question Video: Finding the Values Where the Tangent Function Is Undefined | Nagwa

Question Video: Finding the Values Where the Tangent Function Is Undefined Mathematics • First Year of Secondary School

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Find the values of π in radians such that the function π(π) = tan (3π) is undefined.

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Video Transcript

Find the values of π in radians such that the function π of π equals tan of three π is undefined.

To answer this question, we first need to consider the domain of the tangent function. The domain of the function π of π, which is equal to tan π, when working in radians is all real numbers except for π is equal to π over two plus ππ, where π is an integer. So thatβs π over two plus integer multiples of π. In other words, the tangent function is undefined when π is equal to any of these values, when π is equal to π over two plus any integer multiple of π. We should recall that these values of π correspond to the positions of the vertical asymptotes on the graph of tan π.

However, in this question weβre working with the function π of π is equal to tan of three π. So to find where this function is undefined, we need to consider when three π is equal to any of these values. So weβre looking for when three π is equal to π over two plus ππ, where π is an integer. Dividing both sides of this equation by three, we find that π of π will be undefined when π is equal to π by six plus ππ over three. So weβve completed the problem. The function π of π which is equal to tan of three π is undefined when π is equal to π by six plus ππ over three, where π represents any integer.

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