Sin^-1(-√3/2)
To find the value of inverse sine of -√3/2, we need to understand what inverse sine means and use a trigonometric identity
To find the value of inverse sine of -√3/2, we need to understand what inverse sine means and use a trigonometric identity.
Inverse sine, denoted as sin^(-1) or arcsin, is the opposite operation of sine. It helps us find the angle whose sine is a given value. In other words, if sin(x) = y, then sin^(-1)(y) = x.
In this case, we want to find the angle whose sine is -√3/2. To do this, we will use the reference angle for sine and the unit circle.
The reference angle for sine is the acute angle formed between the terminal side of an angle and the x-axis in the unit circle. It helps us find the positive value of the angle with the same sine. The reference angle for sine can be found by taking the inverse sine of the absolute value of the given sine.
sin^(-1)(√3/2) = π/3 (since the sine of π/3 is √3/2)
However, we are looking for the negative value of this angle, which would be in the third quadrant of the unit circle. In the third quadrant, both the x and y coordinates are negative.
So, the solution to sin^(-1)(-√3/2) is -π/3. Therefore, the angle whose sine is -√3/2 is -π/3.
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