Sin^-1(-1)
To find the value of sin^-1(-1), we need to determine the angle whose sine is equal to -1
To find the value of sin^-1(-1), we need to determine the angle whose sine is equal to -1.
The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The sine function typically ranges between -1 and 1, and the angle lies within the interval [-π/2, π/2] or [-90°, 90°].
For sin^-1(-1), we are looking for an angle whose sine value is -1. Since the sine function is negative in the third and fourth quadrants of the unit circle, we know that the angle lies in either the third or fourth quadrant.
In the third quadrant, the y-coordinate of a point on the unit circle is negative, and this corresponds to a negative sine value. One angle that has a sine of -1 in this quadrant is -π/2 radians (-90°).
In the fourth quadrant, the x-coordinate of a point on the unit circle is positive, and the sine function is again negative. One angle that has a sine of -1 in this quadrant is 3π/2 radians (270°).
Therefore, sin^-1(-1) can either be -π/2 radians or 3π/2 radians (-90° or 270°), depending on the context or the specific range of the inverse sine function being considered.
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