Does Sin^-1(-x)=-Sinx? Is it true or false and explain.
No, of course not. How can 1/sin(-x)=-sinX
-1/sin(x)=-sinX
In general not true, unless...
1=sin^2x
1=sin (x)
x=PI/2 or 2PI + PI/2, ...
I assume you do not mean for sin^-1 INVSINE, or ARCSIN, but 1/sin(x)
In case you mean
Does arcsin (-x) = sin x,
that would be true for x = 0.
In general, it is not true
The statement "Sin^-1(-x)=-Sinx" is false.
Let's break it down to understand why it's false.
First, the expression "Sin^-1(-x)" represents the inverse sine function. It gives you the angle whose sine is equal to -x. In other words, it returns the angle whose sine value, when plugged into the sine function, yields -x.
On the other hand, "Sinx" simply represents the sine function applied to the angle x. It gives you the value of the sine of the angle x.
In general, the inverse function and the original function are not the same. They have different properties and give different results.
To prove this, we can use an example. Let's say x is equal to 30 degrees. The sine of 30 degrees is 0.5.
Now, let's see what happens when we apply the inverse sine function, Sin^-1(-0.5), to -0.5. It will give us the angle whose sine is equal to -0.5.
When we calculate Sin^-1(-0.5), we find that the angle is -30 degrees, not 30 degrees. Therefore, Sin^-1(-0.5) is -(-0.5)=-0.5, not equal to 0.5.
Hence, we have shown that Sin^-1(-x) is not equal to -Sinx. The statement is false.
To verify these calculations and understand why the inverse sine function returns a negative angle in this case, you can use a scientific calculator or mathematical software that has functions like sine and inverse sine built-in.