Sqrt of 9sin^2x
Is the answer |3sinx|?
Is the three included in the absolute value sign? My teacher is very picky and I need to fully understand this concept. Thank you.
The answer has to be positive as you know.
3 is already positive.
sin x might be negative though
so
3 |sin x| would be more appropriate than |3 sin x|
although of course they are the same.
To find the square root of 9sin^2x, we can start by simplifying the expression inside the square root.
Since sin^2x is the square of sinx, we can rewrite the expression as sqrt(9(sin^2x)).
Taking the square root of 9 gives us 3, so we have 3sqrt(sin^2x).
Now, let's address the absolute value. Since sin^2x is always positive, we can remove the absolute value signs from the expression.
Therefore, the final answer is 3sinx. The absolute value is not necessary in this case because sin^2x is always positive.