What is arctan 3/4 in degrees?
Understand the Problem
The question is asking for the angle in degrees whose tangent is 3/4. We will calculate the arctangent of 3/4 and convert the result from radians to degrees if necessary.
Answer
36.87 degrees
Answer for screen readers
The final answer is approximately 36.87 degrees
Steps to Solve
- Calculate the arctangent in radians
Use a calculator or an arctangent function to find the angle whose tangent is 3/4.
$$ heta = \arctan\left(\frac{3}{4}\right)$$
- Convert radians to degrees
Multiply the angle in radians by (\frac{180}{\pi}) to convert it to degrees.
$$\theta_{\text{degrees}} = \theta_{\text{radians}} \times \frac{180}{\pi}$$
- Perform the multiplication
Let’s calculate:
$$\theta_{\text{radians}} = \arctan\left(\frac{3}{4}\right) \approx 0.6435 \text{ radians}$$
Now convert this to degrees:
$$\theta_{\text{degrees}} \approx 0.6435 \times \frac{180}{\pi} \approx 36.87^{\circ}$$
The final answer is approximately 36.87 degrees
More Information
The arctangent function returns an angle whose tangent is the specified value. In practical applications, it is common in fields such as trigonometry, physics, and engineering.
Tips
Make sure your calculator is set to the correct mode (radians or degrees) when performing trigonometric calculations.
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