Answer:
3pi/4 and -pi/4
Step-by-step explanation:
We can simplify -6/6 to -1.
Therefore, this function can be simplified to arctan(-1).
Recall that the meaning of arctan is to find a value that will get the value inside the parenthesis when taken the tangent of it. In other words, tan(x) = -1.
Recall that tan(x) = sin(x)/cos(x). Now recall that sin(pi/4) and cos(pi/4) are both sqrt(2)/2, meaning that tan(pi/4) is 1. To make it -1, we can either make sin(x) -1 while keeping cos(x) 1, or the other way around.
If x is -pi/4, cos(x) will still be 1, but sin(x) will be -1, so tan(-pi/4) will be -1.
If x is 3pi/4, cos(x) will be -1, but sin(x) will still be 1, so tan(3pi/4) will be -1.
Side note: there are still infinite more answers. You can attain them by adding or subtracting 2pi as many times as you want from 3pi/4 or -pi/4 and still get an arctan of -1.
So whole numbers include the negative numbers, the zero and the positive numbers.
We will examine each category,
1- For the negative numbers:
multiplying a negative number by a positive value will result is a negative value (negative values are less than positive values of course). Therefore, multiplying any negative number by 400 will give a negative value which will make the desired statement false.
2- For the zero:
multiplying any number by a zero will give a result of zero which is again less than positive numbers. So, if we multiply 400 by a zero, the result will be zero which will again make the desired statement false.
3- For positive numbers:
multiplying two positive numbers will result in a positive value. Since 400 is already greater than 15, therefore, multiplying 400 by any positive value will keep the statement true. Since we are looking for the smallest whole number, therefore, we will choose that number to be 1 which will give 400 when multiplied by 400 (this is the smallest possible value).
The answer is 1.
