arcsin(1/4)
Understand the Problem
The question is asking for the arcsine (inverse sine) of 1/4. This involves determining the angle whose sine value is 1/4. The solution will typically result in an angle in radians or degrees.
Answer
The solution is approximately \( 0.2527 \) radians or \( 14.477 \) degrees.
Answer for screen readers
The value of ( x = \arcsin\left(\frac{1}{4}\right) ) is approximately ( 0.2527 ) radians or ( 14.477 ) degrees.
Steps to Solve
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Identify the function To solve for the arcsine of ( \frac{1}{4} ), we use the function: $$ x = \arcsin\left(\frac{1}{4}\right) $$ This means we are looking for an angle ( x ) such that ( \sin(x) = \frac{1}{4} ).
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Use a calculator to find the value Now we will compute the arcsin value using a calculator or a programming tool that has the arcsine function. Ensure the calculator is in the right mode (degrees or radians) according to the desired output. For example, using a scientific calculator: $$ x \approx 0.2527 \text{ radians} \text{ or } 14.477 \text{ degrees} $$
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Interpret the result The arcsin function returns values typically between ( -\frac{\pi}{2} ) and ( \frac{\pi}{2} ) (or -90° to 90°). In this case, since ( \frac{1}{4} ) is positive, the angle ( x ) will be in the first quadrant.
The value of ( x = \arcsin\left(\frac{1}{4}\right) ) is approximately ( 0.2527 ) radians or ( 14.477 ) degrees.
More Information
The arcsine function, or inverse sine, tells you what angle corresponds to a specific sine value. It's often used in triangles to find unknown angles when one knows the lengths of the sides.
Tips
- A common mistake is to forget to check whether the calculator is set to degrees or radians, which can lead to confusion in the answer.
- Another mistake is assuming that all sine values correspond to acute angles; while this is true for positive values within ( 0 ) to ( 1 ), arcsine yields angles in the interval ([-90^\circ, 90^\circ]).
