Solved on Jan 05, 2024

Find the cotangent of 14 degrees.

STEP 1

Assumptions
1. The problem is to find the value of $\cot 14^\circ$ .
2. The cotangent function is the reciprocal of the tangent function.
3. The angle is given in degrees.

STEP 2

To find $\cot 14^\circ$ , we will use the relationship between cotangent and tangent.
$\cot \theta = \frac{1}{\tan \theta}$

STEP 3

Now, we will apply this relationship to the angle $14^\circ$ .
$\cot 14^\circ = \frac{1}{\tan 14^\circ}$

STEP 4

Since $\tan 14^\circ$ is not a standard angle that we can easily compute, we will use a calculator to find its value.

STEP 5

After using a calculator, we find that
$\tan 14^\circ \approx 0.2493$

STEP 6

Now, take the reciprocal of the tangent value to find the cotangent.
$\cot 14^\circ = \frac{1}{0.2493}$

STEP 7

Calculate the value of $\cot 14^\circ$ .
$\cot 14^\circ \approx \frac{1}{0.2493} \approx 4.0108$
Therefore, $\cot 14^\circ \approx 4.0108$ .

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Find the cotangent of 14 degrees.

STEP 1

Assumptions
1. The problem is to find the value of $\cot 14^\circ$ .
2. The cotangent function is the reciprocal of the tangent function.
3. The angle is given in degrees.

STEP 2

To find $\cot 14^\circ$ , we will use the relationship between cotangent and tangent.
$\cot \theta = \frac{1}{\tan \theta}$

STEP 3

Now, we will apply this relationship to the angle $14^\circ$ .
$\cot 14^\circ = \frac{1}{\tan 14^\circ}$

STEP 4

Since $\tan 14^\circ$ is not a standard angle that we can easily compute, we will use a calculator to find its value.

STEP 5

After using a calculator, we find that
$\tan 14^\circ \approx 0.2493$

STEP 6

Now, take the reciprocal of the tangent value to find the cotangent.
$\cot 14^\circ = \frac{1}{0.2493}$

STEP 7

Calculate the value of $\cot 14^\circ$ .
$\cot 14^\circ \approx \frac{1}{0.2493} \approx 4.0108$
Therefore, $\cot 14^\circ \approx 4.0108$ .

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Find the cotangent of 14 degrees.

STEP 1

Assumptions1. The problem is to find the value of cot⁡14∘\cot 14^\circcot14∘.2. The cotangent function is the reciprocal of the tangent function.3. The angle is given in degrees.

STEP 2

To find cot⁡14∘\cot 14^\circcot14∘, we will use the relationship between cotangent and tangent.cot⁡θ=1tan⁡θ\cot \theta = \frac{1}{\tan \theta}cotθ=tanθ1​

STEP 3

Now, we will apply this relationship to the angle 14∘14^\circ14∘.cot⁡14∘=1tan⁡14∘\cot 14^\circ = \frac{1}{\tan 14^\circ}cot14∘=tan14∘1​

STEP 4

Since tan⁡14∘\tan 14^\circtan14∘ is not a standard angle that we can easily compute, we will use a calculator to find its value.

STEP 5

After using a calculator, we find thattan⁡14∘≈0.2493\tan 14^\circ \approx 0.2493tan14∘≈0.2493

STEP 6

Now, take the reciprocal of the tangent value to find the cotangent.cot⁡14∘=10.2493\cot 14^\circ = \frac{1}{0.2493}cot14∘=0.24931​

STEP 7

Calculate the value of cot⁡14∘\cot 14^\circcot14∘.cot⁡14∘≈10.2493≈4.0108\cot 14^\circ \approx \frac{1}{0.2493} \approx 4.0108cot14∘≈0.24931​≈4.0108Therefore, cot⁡14∘≈4.0108\cot 14^\circ \approx 4.0108cot14∘≈4.0108.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions
1. The problem is to find the value of $\cot 14^\circ$ .
2. The cotangent function is the reciprocal of the tangent function.
3. The angle is given in degrees.

To find $\cot 14^\circ$ , we will use the relationship between cotangent and tangent.
$\cot \theta = \frac{1}{\tan \theta}$

Now, we will apply this relationship to the angle $14^\circ$ .
$\cot 14^\circ = \frac{1}{\tan 14^\circ}$

Since $\tan 14^\circ$ is not a standard angle that we can easily compute, we will use a calculator to find its value.

After using a calculator, we find that
$\tan 14^\circ \approx 0.2493$

Now, take the reciprocal of the tangent value to find the cotangent.
$\cot 14^\circ = \frac{1}{0.2493}$

Calculate the value of $\cot 14^\circ$ .
$\cot 14^\circ \approx \frac{1}{0.2493} \approx 4.0108$
Therefore, $\cot 14^\circ \approx 4.0108$ .