What is the positive value of P in the interval [ 0 ° , 90 ° ) \left[0\degree,90\degree\right) [ 0° , 90° ) that will make the following statement true? Express the answer in four decimal places. cot P = 5.2371 \cot P=5.2371 cot P = 5.2371

Let's give this problem a try. Here, we are asked what is the positive value for p in the interval from 0 degrees to 90 degrees that will make the following statement true. Express the answer in 4 decimal places. So what we're given is the cotangent of p is equal to 5.2371, and we're asked to find p. Now to solve this problem, there's not a lot I can do if we have cotangent p by itself because it's not like there's really an inverse cotangent that we know well or can plug into our calculators. But we can recall that there's a reciprocal identity for the cotangent. So the cotangent is the same thing as one over the tangent. So cotangent of p is 1 over tangent p, and this whole thing equals 5.2371. Now from here, I'm going to see if I can get the tangent p by itself. And I can first multiply tangent p on both sides of this equation. If I do this, I will get the tangent p's to cancel on the left side, and this should be a capital p over here. And this means that one is going to equal 5 point 2371 times the tangent of p. Now from here I'm going to take this 5.2371 and divide it on both sides of the equation. So we'll divide it on the right side and on the left side, so 5.237 1, and this will get the 5.237 ones to cancel on the right. So we're going to end up with tangent p is equal to 1 over 5 point 2371. Now at this point we've gotten tangent p by itself, and our real goal in this problem is to find p. So I can isolate this p by taking the inverse tangent on both sides of this equation. If I take the inverse tangent that will get the tangent to cancel leaving me with just p, and p is going to equal the inverse tangent of 1 divided by this number 5.2 371. And this right here is the expression for p, but we need to find an actual number here and round it to 4 decimal places. And to do this, what you first wanna do is you wanna make sure you're in the right mode because notice that our interval is given in degrees so you want to make sure you are in degree mode on your calculator before plugging this value in. Now once you have figured out and set your calculator in degree mode, you're then going to plug the inverse tangent by pressing second and then the tangent key and then plug in this fraction, and that should give you that p is equal to 10.8102, and this decimal keeps going on. But notice from here that we're asked around 4 decimal places, so I'm stopping right there at 2, meaning this is our answer for p. So that is how you can find this value and this missing variable. Hope you found this video helpful.

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

Trigonometry

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

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Multiple Choice

What is the positive value of P in the interval $\left[0\degree,90\degree\right)$ that will make the following statement true? Express the answer in four decimal places.
$\cot P=5.2371$

$55.8102°$

$34.1898°$

$10.8102°$

$79.1898°$

Verified step by step guidance

Understand that the cotangent function, $ \cot P $, is the reciprocal of the tangent function, $ \tan P $. Therefore, $ \cot P = 5.2371 $ implies $ \tan P = \frac{1}{5.2371} $.

Recognize that the problem asks for the angle $ P $ in the interval $[0^\circ, 90^\circ)$ that satisfies $ \cot P = 5.2371 $.

Use the inverse tangent function to find $ P $. Since $ \tan P = \frac{1}{5.2371} $, calculate $ P = \tan^{-1}\left(\frac{1}{5.2371}\right) $.

Ensure that the calculated angle $ P $ is within the specified interval $[0^\circ, 90^\circ)$.

Compare the calculated angle with the given options: 55.8102°, 34.1898°, 10.8102°, and 79.1898°, to determine which one matches the calculated value of $ P $.