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 zero degrees to 90 degrees that will make the following statement true. Express the answer in four 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 one 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. This should be a capital p over here. And this means that one is going to equal 5.2371 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 5.2371, 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 one over 5.2371. 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 one divided by this number 5.2371. And this right here is the expression for p. But we need to find an actual number here and round it to four 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 four decimal places, so I'm stopping right there at two, 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.

12. Trigonometric Functions

Trigonometric Functions on Right Triangles

Business Calculus

12. Trigonometric Functions

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

Step 1: Recall the definition of cotangent. The cotangent function is defined as cot(P) = 1 / tan(P). This means we are looking for an angle P in the interval [0°, 90°) such that cot(P) = 5.2371.

Step 2: To solve for P, take the reciprocal of cot(P) to find tan(P). This gives tan(P) = 1 / 5.2371. Compute this value to determine the tangent of the angle.

Step 3: Use the arctangent function (tan⁻¹) to find the angle P. Specifically, P = tan⁻¹(1 / 5.2371). Ensure your calculator is set to degrees, as the problem specifies the interval in degrees.

Step 4: Verify that the resulting angle P lies within the interval [0°, 90°). If it does not, adjust the angle accordingly to ensure it is within the specified range.

Step 5: Round the resulting angle P to four decimal places, as required by the problem. This will give you the positive value of P that satisfies cot(P) = 5.2371.