Finding the Inverse Sine of -1/2: Calculator and Unit Circle Methods

Sin^-1(-1/2)

To find the inverse sine (sin^-1) of -1/2, we need to find the angle whose sine is equal to -1/2

To find the inverse sine (sin^-1) of -1/2, we need to find the angle whose sine is equal to -1/2.

The inverse sine function, denoted as sin^-1 or arcsin, returns the angle in radians or degrees whose sine is equal to the given value.

To find the angle, we can use either a calculator or the unit circle.

Using a calculator:
1. Turn on your calculator and make sure it is set to degrees or radians based on your preference.
2. Enter -1/2 in the calculator using the fraction or decimal representation.
3. Press the inverse sine function key (sin^-1 or arcsin), typically denoted as “sin^-1” or “asin”.
4. The calculator will display the result as an angle measure.

If using the unit circle:
1. Draw a unit circle (a circle with a radius of 1) on a piece of paper or visualize it in your mind.
2. Locate the point (-1/2, y) on the coordinate plane. On the unit circle, the y-coordinate represents the sine of the angle.
3. Note that at two different locations on the unit circle, the y-coordinate is -1/2. These two angles are 7π/6 (210 degrees or 2π + 7π/6) and 11π/6 (330 degrees or 2π + 11π/6).
4. Therefore, sin^-1(-1/2) equals 7π/6 or 11π/6, depending on whether you are working in radians or degrees.

Thus, the answer to sin^-1(-1/2) is either 7π / 6 radians or 210 degrees, or 11π / 6 radians or 330 degrees, depending on your preferred unit of measurement.

More Answers: