Final answer:
To determine if the inverse sine is 180 degrees minus the answer, you need to understand how the sine function and its inverse work. The sine function gives you the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. The inverse sine function, also known as arcsine or sin^(-1), gives you the angle whose sine is a given ratio.
Step-by-step explanation:
To determine if the inverse sine is 180 degrees minus the answer, you need to understand how the sine function and its inverse work. The sine function gives you the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
The inverse sine function, also known as arcsine or sin^(-1), gives you the angle whose sine is a given ratio. So, if you have an angle A and you take the inverse sine of its sine, you should get back the same angle A.
Now, if you want to find the angle that is 180 degrees minus a given angle, you can use the properties of angles. Subtracting an angle from 180 degrees gives you its supplement angle. The supplement of an angle is the angle that, when added to the original angle, gives you a straight line angle of 180 degrees. So, if you take the inverse sine of a given angle A and subtract it from 180 degrees, you should get its supplement angle.
For example, let's say you have an angle A = 30 degrees. Taking the inverse sine of 30 degrees gives you sin^(-1)(sin(30)) = sin^(-1)(0.5) = 30 degrees. This confirms that the inverse sine of an angle is indeed equal to the angle itself. Now, if you subtract the inverse sine of 30 degrees from 180 degrees, you get 180 - 30 = 150 degrees, which is the supplement angle of 30 degrees.