Problem 891 Find \(\arcsin (1 / 2)\).... [FREE SOLUTION]

Chapter 28: Problem 891

Find \(\arcsin (1 / 2)\).

Short Answer

Expert verified

\(\arcsin\left(\frac{1}{2}\right) = 30^{\circ} \text{ or } \frac{\pi}{6} \text{ radians}\)

Step by step solution

Recall properties of the sine function

Recall that the sine function is positive in the first and second quadrants. Also, the sine value is equal for an angle and its supplementary angle (180 - angle). This assures that there is an angle in the first quadrant for which the sine value is 1/2, and we need to find that angle.

Use the sine value of prominent angles

Consider the common angles in degrees: 30, 45, 60, and 90. We know the following: \(\sin(30^{\circ}) = \frac{1}{2}\) \(\sin(45^{\circ}) = \frac{\sqrt{2}}{2}\) \(\sin(60^{\circ}) = \frac{\sqrt{3}}{2}\) \(\sin(90^{\circ}) = 1\) From the given sine values, we can see that the sine of 30 degrees is equal to 1/2. Therefore, the angle we are looking for is 30 degrees or in radians.

Convert degrees to radians

To convert the angle from degrees to radians, use the formula: \[Radians = Degrees * \frac{\pi}{180}\] In our case, the angle we found is 30 degrees. Plug in the value and solve for radians: \[Radians = 30 * \frac{\pi}{180} = \frac{\pi}{6}\]

Write down the final solution

We found that the angle for which the sine value is 1/2 and lies within the allowed range of the arcsine function is 30 degrees or \(\frac{\pi}{6}\) radians. Thus, \[\arcsin\left(\frac{1}{2}\right) = 30^{\circ} \text{ or } \frac{\pi}{6} \text{ radians}\]

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91影视

Find \(\arcsin (1 / 2)\).

Short Answer

Step by step solution

Recall properties of the sine function

Use the sine value of prominent angles

Convert degrees to radians

Write down the final solution

One App. One Place for Learning.

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