Graphing Calc Help: Typing cos^2 x = 2

  • Thread starter Liquidice_69
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In summary, you can type cos^2 x = 2 into a graphing calculator by entering the cosine followed by the square root. There are many solutions to this equation, but if you're looking for a specific one you can use the zoom feature on your calculator to find it.
  • #1
Liquidice_69
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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.
 
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  • #2
Do you know what a function squared means? It means the function times itself..
 
  • #3
ya i know, but i just want to know how to solve cos^2 x = 2 but i don't know how
 
  • #4
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 cos2x= 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 [tex]cos(x)= \sqrt{2}[/tex]. BUT you also have to know that a negative number, squared, is a positive number [tex]cos x= -\sqrt{2}[/tex] is also a possibility. Now, the "inverse" of cosine in arccos or cos-1 so from [tex]cos x= \sqrt{2}[/tex] 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!
 
  • #5
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.
 
  • #6
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
 
  • #7
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
 
  • #8
but i thought

cos(x)^2 doesn't equal cos^2 (x)
 
  • #9
[tex] cos^2(x) = cos(x)^2 = cos(x)cos(x) \neq cos(x^2) [/tex]
 
  • #10
ok thxs

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

[tex] cos^2(x) = 2 [/tex]

[tex]x= cos^{-1}(\sqrt{2}): [/tex]


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

Related to Graphing Calc Help: Typing cos^2 x = 2

What is a graphing calculator?

A graphing calculator is a specialized calculator that is capable of plotting graphs and performing various mathematical functions. It typically has a larger screen and more advanced features than a regular calculator.

How do I type "cos^2 x = 2" into a graphing calculator?

To type "cos^2 x = 2" into a graphing calculator, you will need to use the appropriate buttons or symbols on your calculator. First, enter the "cos" function by pressing the "cos" button or typing "cos(" followed by the value of x. Then, use the "^" button or symbol to indicate the exponent. Finally, type in the value of 2 after the "=" sign.

Why is the graphing calculator not giving me the correct answer for "cos^2 x = 2"?

If your graphing calculator is not giving you the correct answer for "cos^2 x = 2", it could be due to a few reasons. First, make sure that you have correctly entered the equation using the appropriate buttons or symbols. Also, check that your calculator is set to the correct mode (degrees or radians) for the given equation. If everything appears to be correct and you are still not getting the correct answer, it could be a malfunction or error with your calculator.

Can I solve for x using a graphing calculator for "cos^2 x = 2"?

Yes, you can solve for x using a graphing calculator for "cos^2 x = 2". To do so, you will need to use the "solve" function on your calculator. This function allows you to input an equation and solve for a specified variable, in this case, x. Refer to your calculator's manual for specific instructions on how to use the "solve" function.

Are there any other ways to represent "cos^2 x = 2" on a graphing calculator?

Yes, there are other ways to represent "cos^2 x = 2" on a graphing calculator. One alternative is to use the equivalent form of the equation, "1 - sin^2 x = 2". You can also use the "cos^-1" (inverse cosine) function to solve for x, which would give you x = ±1.047197551 radians or ±60 degrees.

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