what is the approximate solution to 2cos(x)+x=0 to the nearnest 100th?

Answer 1

Option a: use one of the fancy calculators around nowadays.
Option b:
Ok, we need at least a reasonable guess to get going. Lets draw a graph. But how do you draw a graph of 2cos(x) + x? We don't. We draw a graph of 2cos(x), and another graph of -x, and see where they are equal - because thats the point we're looking for. Don't forget to use radians, since you can't add a number to a degree.
The solution looks like it is around -1 or so. Now we can do a bit more guessing.
Putting -1 into that equation gives 0.0806. Lets try -0.9. Whoops - that gives 0.34, which is getting even worse. How about -1.1? Ahha! That gives -0.19, so we know the answer is between -1.1 and -1.0.
We can keep narrowing it down in this way. Try -1.05: thats negative, so we're between -1.0 and -1.05. Try -1.02: thats positive, so we're between -1.02 and -1.05. Try -1.03: thats negative, but nearly 0. So we're between -1.02 and -1.03.
We're nearly there - try -1.025. thats positive, so we're done! We know the answer is between -1.025 and -1.03, so it must be -1.03 to the nearest 100th.
Thats quite a bit of work, but its not too bad. There are faster ways to do it, but they're a bit more complicated.

Answer 2

About -1.029867 so to the 100th place -1.03.

Answer 3

In degrees it is -2.00

In radians, -1.03

Answer 4

x=-1.03