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Use a calculator to evaluate each expression to the nearest tenth of a degree. \( \arcsin (0.4124)=\square \)

Ask by Chan Tyler. in the United States
Feb 05,2025

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Answer

\( \arcsin(0.4124) = 24.4^\circ \)

Solution

To evaluate \( \arcsin(0.4124) \) to the nearest tenth of a degree, follow these steps: 1. **Understand the Function:** - The arcsine function, \( \arcsin(x) \), returns the angle whose sine is \( x \). - The output will be in degrees since the question specifies the answer in degrees. 2. **Calculate Using a Calculator:** - Input \( 0.4124 \) into the arcsine function on your calculator. - Ensure your calculator is set to **degrees** mode. 3. **Computation:** \[ \arcsin(0.4124) \approx 24.4^\circ \] 4. **Final Answer:** \[ \arcsin(0.4124) = 24.4^\circ \] **Answer:** \( \arcsin(0.4124) = 24.4^\circ \)

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Bonus Knowledge

When you enter \( \arcsin(0.4124) \) into a calculator, you'll find that it approximates to about \( 24.4^\circ \) when rounded to the nearest tenth of a degree. This means that the angle whose sine is \( 0.4124 \) is approximately \( 24.4 \) degrees! Did you know that the arcsine function is often used in various fields such as physics and engineering? For instance, it can help determine angles in right triangles when you know the ratio of the opposite side to the hypotenuse. This makes it an essential tool in many real-world applications involving angles and triangles!

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