arctan 0.1
Understand the Problem
The question is asking for the arctangent of 0.1, which is a trigonometric function seeking an angle whose tangent is 0.1. This calculation is typically performed using a calculator or trigonometric tables.
Answer
$0.09967$ radians or $5.71$ degrees.
Answer for screen readers
The answer is approximately $0.09967$ radians or $5.71$ degrees.
Steps to Solve
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Identify the function We are calculating the arctangent of $0.1$. The arctangent function is denoted as $\tan^{-1}(x)$ or $\text{arctan}(x)$.
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Set up the calculation We need to find $\text{arctan}(0.1)$. This can be done using a scientific calculator or software that can compute inverse trigonometric functions.
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Compute the value Using a calculator, input the value: $$ \theta = \text{arctan}(0.1) $$
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Record the result Upon calculation, you'll find that: $$ \theta \approx 0.099668652 \text{ radians} $$
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Convert to degrees if necessary To convert radians to degrees, use the conversion formula: $$ \text{degrees} = \theta \times \frac{180}{\pi} $$
The answer is approximately $0.09967$ radians or $5.71$ degrees.
More Information
The arctangent function gives you the angle whose tangent is a specific value. For small values like $0.1$, the angle is quite small, reflecting the fact that tangent values rise steeply for angles near $45^\circ$ (or $\pi/4$ radians).
Tips
- Misunderstanding the function: Always ensure you understand that arctangent asks for an angle whose tangent gives the supplied value, and not the reverse.
- Calculation errors: Double-check entries in the calculator to ensure correct results, especially when converting from radians to degrees.
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