Find the value of the inverse function in degrees, using the trigonometric table.
arcsin (0.5299)
26°
38°
20°
32°
The correct answer and explanation is:
The correct answer is 32°.
Explanation:
The arcsine function (denoted as arcsin or sin⁻¹) is the inverse of the sine function. It gives the angle whose sine is equal to a given value. In this case, we are looking for the angle whose sine value is 0.5299.
- Understanding arcsin: The arcsine function outputs an angle in the range of -90° to 90°, meaning it gives us angles in the first or fourth quadrant. The given value 0.5299 represents the sine of an angle. To find this angle, we refer to the sine table or use a calculator to find the corresponding angle.
- Using a Trigonometric Table: From a standard trigonometric table, we can look for the sine value closest to 0.5299. The sine of 32° is approximately 0.5299, which matches the value given in the problem.
- Verification: Using a calculator, if we input
arcsin(0.5299), we get the result as approximately 32°. This confirms that the angle whose sine is 0.5299 is indeed 32°. - Other Options: The other values given (26°, 38°, and 20°) do not have sine values close to 0.5299. For example:
- sin(26°) ≈ 0.4384
- sin(38°) ≈ 0.6157
- sin(20°) ≈ 0.3420
Since none of these values match 0.5299, the correct answer is 32°.
In summary, using the trigonometric table or a calculator, we find that the angle whose sine is 0.5299 is 32°, making it the correct solution.