cdhotfire said:a friend he said it was pi/2, i guess he was wrong because i see now way of getting that, well for these problems like the one above i just get trig function inside the para and that's the awnser. Can i make that generalization?
oh, and thxs for the help
To solve arcsin(sin 3π), you can follow these steps:
1. Rewrite the given equation as arcsin(sin x) = 3π
2. Use the identity arcsin(sin x) = x to rewrite the equation as 3π = x
3. Simplify the equation to x = 3π
4. Since the domain of arcsin is between -π/2 and π/2, we need to find an equivalent angle in this range.
5. Use the periodicity of sine function to find an equivalent angle in the desired range. In this case, we can use the fact that sin(3π) = 0 to get x = 0.
6. Therefore, the solution to arcsin(sin 3π) is x = 0.
No, arcsin(sin 3π) has only one solution. This is because the arcsin function is defined as the inverse of the sine function, and by definition, the inverse function has a unique output for each input. In this case, the input is sin 3π, which has only one value (0) and therefore, the output of arcsin(sin 3π) is also unique.
You can check your solution by substituting it back into the original equation and seeing if it satisfies the equation. In this case, if we substitute x = 0 into the equation arcsin(sin x) = 3π, we get arcsin(sin 0) = 3π, which simplifies to 0 = 3π. Since this is not a true statement, we can conclude that our solution of x = 0 is incorrect.
Yes, the solution to arcsin(sin 3π) can be expressed in both radians and degrees. In radians, the solution is x = 0. In degrees, the solution is x = 0°. However, it is important to note that the input to the arcsin function is always a ratio and not an angle, so it may not make sense to express the solution in degrees.
Yes, you can use a calculator to solve arcsin(sin 3π). Most scientific calculators have a function for arcsin, which is usually denoted as "sin^-1". Simply enter "sin^-1(0)" and you will get the solution of 0.