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