Find a value of

alphaα

in the interval

​[0degrees°​,

90degrees°​]

that satisfies the given statement.

Bold cot**cot**

alphaαequals=1.2868639

We are tasked with finding the value of \( \alpha \) (in degrees) that satisfies the equation:

\[
\cot(\alpha) = 1.2868639
\]

### Step 1: Recall the definition of the cotangent function.
The cotangent of an angle \( \alpha \) is the reciprocal of the tangent of that angle:

\[
\cot(\alpha) = \frac{1}{\tan(\alpha)}
\]

Thus, the equation can be rewritten as:

\[
\tan(\alpha) = \frac{1}{1.2868639}
\]

### Step 2: Calculate the reciprocal of \( 1.2868639 \).

\[
\tan(\alpha) = \frac{1}{1.2868639} \approx 0.777059
\]

### Step 3: Find \( \alpha \) using the arctangent function.

Now we use the inverse tangent (arctan) to find \( \alpha \):

\[
\alpha = \tan^{-1}(0.777059)
\]

Using a calculator:

\[
\alpha \approx 37.999^\circ
\]

So, the value of \( \alpha \) that satisfies \( \cot(\alpha) = 1.2868639 \) is approximately:

\[
\alpha \approx 38.00^\circ
\]

### Would you like more details or have any questions?

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Here are 5 related questions for further exploration:

1. What is the value of \( \alpha \) in radians for this solution?
2. How would the solution change if the cotangent value were negative?
3. What is the relationship between cotangent and sine/cosine?
4. Can you find the secant of the same angle \( \alpha \)?
5. How does the tangent of this \( \alpha \) compare to the cotangent?

**Tip:** To solve trigonometric equations, always remember to ensure your calculator is set to the correct angle mode (degrees or radians).

Find a value of α in the interval [0°, 90°] that satisfies the given statement: cot(α) = 1.2868639.

Learn how to find the value of α in degrees that satisfies cot(α) = 1.2868639. This problem explores key trigonometric concepts, such as the reciprocal relationship between cotangent and tangent, and uses the arctangent function to calculate the solution.

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