Question

How do I resolve cos>-2?

Answer 1

Nice glasses.

Answer 2

Sorry cosx>-2

Answer 3

ahaha thanks xD

Answer 4

@naylah what do you mean by "solve" ?

Answer 5

keep in mind that \(\bf -1 \le cos(\theta)\le 1\)

Answer 6

I am studying the derivative of y=2x+sinx which is y'=2+cosx. How should I operate?

Answer 7

You welcome. Now you need to find the values for which the cos is greater than 2. Which is the empty set. Because the cosine of any number is between -1 and 1

Answer 8

In order to see the crescence and decrescence of the function

Answer 9

You need to set the first derivative to zero, then split it's domain and check whether the second derviative in those intervals is greater or smaller than zero

Answer 10

Can you show me how it's done please?

Answer 11

The graph of this function looks like this.

Answer 12

So you can see that it's increasing all the way

Answer 13

This is a better picture of it.

Answer 14

Ok

Answer 15

But how do I manage to trace that graph on my own without using that program?

Answer 16

You just start giving x some values (ex. from -10 to 10) and see what y values you get then you print those points in an coordinate system and finally join those points together and there you go the graph is ready. :)

Answer 17

But how can I do it? Can you make a more concrete example?
If I put x=10 then I'll get cos(10)=-2

Answer 18

Sorry if I ask so many questions xD

Answer 19

You can't get -2 for 10. Are you working with degrees,radians or what?

Answer 20

If x=10 you get y = 19.161, if x=9, y=17.089, if x=5, y = 10.284 ...you go on like this.

Answer 21

Isn't there a simpler method?

Answer 22

This is as simple as it gets. No derivatives no slopes and crap...

Answer 23

The problem is that my professor doesn't allow us to use a calculator so I was looking for a method that didn't involve such calculations.

Answer 24

So what exactly is the question there?

Answer 25

I have to study the function y=2x+sinx and trace its graph.

Answer 26

If you just wanna know how it behaves like is it increasing or decreasing then you could use the first derivative. Wherever the first derivative of a function is greater than zero the function is increasing and vice versa. BUT You won't be able to graph a function (like that) without any calculator or graphing software.

Answer 27

Ah ok. Can you show me through the derivative if the function is increasing or not?

Answer 28

\[y \prime > 0\]

Answer 29

for all x in the domain of the function so it is always increasing.

Answer 30

Ah ok. Thanks again!

Answer 31

No problems.