# Question Video: Using the Relationship between Trigonometric Functions of Complementary Angles to Find an Unknowing Angle Mathematics

Find the value of 𝑥 given tan 78° = cot 𝑥.

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### Video Transcript

Find the value of 𝑥 given tan 78 degrees is equal to cot 𝑥.

So the first thing we can use to help us solve this problem is the fact that cot 𝑥 is equal to one over tan 𝑥. So therefore, we can rewrite tan 78 degrees equals cot 𝑥 as tan 78 degrees equals one over tan 𝑥. So then, if we multiply each side of the equation by tan 𝑥, we get tan 𝑥 tan 78 degrees is equal to one.

And then, the next step would be to divide each side of the equation by tan 78 degrees. So we get tan 𝑥 is equal to one over tan 78 degrees. And to find out what 𝑥 is, what we’re gonna do is take the inverse of tan of both sides of the equation. So we get 𝑥 is equal to inverse tan one over tan 78 degrees. And remember, inverse tan is sometimes known as shift tan. And that’s because, on the calculator, you press shift and then the tan button. And that will usually give you the inverse tan. So when you’ve worked out the inverse tan of one over tan 78 degrees, we find out that 𝑥 is equal to 12 degrees.

So therefore, we can say that the value of 𝑥 given that tan 78 degrees is equal to cot 𝑥 is 12 degrees.