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

Video Transcript

Find the values of 𝜃 in radians such that the function 𝑓 of 𝜃 equals tan of three 𝜃 is undefined.

To answer this question, we first need to consider the domain of the tangent function. The domain of the function 𝑔 of 𝜃, which is equal to tan 𝜃, when working in radians is all real numbers except for 𝜃 is equal to 𝜋 over two plus 𝑛𝜋, where 𝑛 is an integer. So that’s 𝜋 over two plus integer multiples of 𝜋. In other words, the tangent function is undefined when 𝜃 is equal to any of these values, when 𝜃 is equal to 𝜋 over two plus any integer multiple of 𝜋. We should recall that these values of 𝜃 correspond to the positions of the vertical asymptotes on the graph of tan 𝜃.

However, in this question we’re working with the function 𝑓 of 𝜃 is equal to tan of three 𝜃. So to find where this function is undefined, we need to consider when three 𝜃 is equal to any of these values. So we’re looking for when three 𝜃 is equal to 𝜋 over two plus 𝑛𝜋, where 𝑛 is an integer. Dividing both sides of this equation by three, we find that 𝑓 of 𝜃 will be undefined when 𝜃 is equal to 𝜋 by six plus 𝑛𝜋 over three. So we’ve completed the problem. The function 𝑓 of 𝜃 which is equal to tan of three 𝜃 is undefined when 𝜃 is equal to 𝜋 by six plus 𝑛𝜋 over three, where 𝑛 represents any integer.