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

Find the value of π₯ given tan 78Β° = cot π₯.

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### Video Transcript

Find the value of π₯ given tan 78 degrees is equal to cot π₯.

So the first thing we can use to help us solve this problem is the fact that cot π₯ is equal to one over tan π₯. So therefore, we can rewrite tan 78 degrees equals cot π₯ as tan 78 degrees equals one over tan π₯. So then, if we multiply each side of the equation by tan π₯, we get tan π₯ 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 π₯ is equal to one over tan 78 degrees. And to find out what π₯ is, what weβre gonna do is take the inverse of tan of both sides of the equation. So we get π₯ is equal to inverse tan one over tan 78 degrees. And remember, inverse tan is sometimes known as shift tan. And thatβs because, on the calculator, you press shift and then the tan button. And that will usually give you the inverse tan. So when youβve worked out the inverse tan of one over tan 78 degrees, we find out that π₯ is equal to 12 degrees.

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