find the exact value of the expression , sin-1(-0.5)
sin -1 as principal values in [-π/2,π/2]
sin -1-.5 = -π/6
To find the exact value of the expression sin^(-1)(-0.5), we need to use the inverse sine function or arcsine.
The inverse sine function, sin^(-1)(x), is the inverse of the sine function sin(x). It returns the angle whose sine is equal to x.
To find the exact value of sin^(-1)(-0.5), we need to determine the angle whose sine is -0.5.
The sine function has the range [-1, 1]. So, we need to find the angle whose sine falls within this range.
Since sin(30°) = 0.5, we can conclude that sin(-30°) = -0.5. Therefore, the angle whose sine is -0.5 is -30°.
So, the exact value of sin^(-1)(-0.5) is -30°.