Graphing Calc Help: Typing cos^2 x = 2

[Liquidice_69]

how do u type cos^2 x = 2 into a graphing calc because when ever use push cos it puts the ( so u can't a ^2 before it.

 

[whozum]

Do you know what a function squared means? It means the function times itself..

 

[Liquidice_69]

ya i know, but i just want to know how to solve cos^2 x = 2 but i don't know how

 

[HallsofIvy]

Unfortunately your calculator isn't going to think for you.

The direct way (what I would consider the "mathematical" way) is to solve the equation yourself then use your calculator to get the number.

You have cos<sup>2x= 2. That means two things have been done to x: take the cosine and then square. To solve the equation, you have to 'back out'- do the opposite of what has been done: the opposite of squareing is square root- from
cos2x= 2 you get $$cos(x)= \sqrt{2}$$. BUT you also have to know that a negative number, squared, is a positive number $$cos x= -\sqrt{2}$$ is also a possibility. Now, the "inverse" of cosine in arccos or cos-1 so from $$cos x= \sqrt{2}$$ you get [tex]x= cos^{-1}(\sqrt{x}): but, again, there are many solutions to the equation. If you have really learned these functions, you could work out a formula for all solutions.

Another way to use a graphing calculator to solve an equation like this is to graph two functions: y= cos2 x and y= 2. The "zoom" into the places where the two graphs cross. Of course, that won't give you a formula that enables you to writed down all solutions but it might let you pass the course without actually having to learn any mathematics!</sup>

 

[whozum]

Its a shame the overuse of calculators. I remember in high school people who would reach for their calculator when asked for the answer to 12+9.

 

[Liquidice_69]

im sry if you think I am not trying but I am not taking a trig course I am just in algebra 2 and my teacher wanted to touch on trig.
But with the calc you said to type in y= cos^2 x but i don't know to do that with my ti 83+ because when i push the cos button in outputs cos( so i can't put a ^2

 

[whozum]

I already told you how to solve this problem.

Hit the y-function button on the top left. Then in the first line press the cos button, in parenthesis enter x, and close the parentheses. Then put ^2 outside.
Alternatively you could enter cos(x)*cos(x) , which equals cos^2(x) = cos(x)^2

 

[Liquidice_69]

but i thought

cos(x)^2 doesn't equal cos^2 (x)

 

[whozum]

$$cos^2(x) = cos(x)^2 = cos(x)cos(x) \neq cos(x^2)$$

 

[Liquidice_69]

ok thxs

so i want to solve this for x over $$[-2pi, 2pi]$$
$$cot(x)cos^2(x) = 2 cot(x)$$

$$cos^2(x) = 2$$

$$x= cos^{-1}(\sqrt{2}):$$


but how do i find all of the solution i am looking for from there