Confused on order of operations for trig

[Eithman]

I am following a video on Khan Academy showing me how to use the law of cosine to find an angle. I filled it in and I have this. 400=6,100-6,000 x COS(?)

My first instinct is to use reverse pemdos to simplify it. 400=100 X COS(?)
And then divide by 100 on both sides to finally get 4 = COS(?)

But in the video they start by subtracting 6,100 to get -5,700 = -6000 X COS(?)
Then they divide by -6000 to end up with. 57/60 = COS (?)
Finally they subtract COS to end up with. COS-1(19/20) = ?
And the answer is 18.19

I know this answer is correct but they seem to be simplifying out of order and I can not understand what I was doing wrong. Could some please explain. Thanks so much!

 

[lev888]

Since multiplication is done before addition/subtraction you can't start with 6,100-6,000. You can't just ignore "x COS"!!!
The fact that you ended up with 4 = COS is a major red flag - cos() can't be equal to 4, it oscillates between -1 and 1.

You might want to review what reverse pemdAs is:
https://d3jc3ahdjad7x7.cloudfront.net/Iar6eXYwv2djtrlkEfxzK7zuM9qqjWkmCVqNyPix7LjdKhfn.pdf

 

[Dr.Peterson]

I am following a video on Khan Academy showing me how to use the law of cosine to find an angle. I filled it in and I have this. 400=6,100-6,000 x COS(?)

My first instinct is to use reverse pemdos to simplify it. 400=100 X COS(?)
And then divide by 100 on both sides to finally get 4 = COS(?)

But in the video they start by subtracting 6,100 to get -5,700 = -6000 X COS(?)
Then they divide by -6000 to end up with. 57/60 = COS (?)
Finally they subtract COS to end up with. COS-1(19/20) = ?
And the answer is 18.19

I know this answer is correct but they seem to be simplifying out of order and I can not understand what I was doing wrong. Could some please explain. Thanks so much!

I suppose you mean "reverse PEMDAS"; but it looks like you didn't actually reverse anything.

Let's take a simpler example:

10 = 4 - 2x
​

In order to evaluate the right-hand side (using PEMDAS) you would multiply x by 2, then subtract from 4. To solve, you need to reverse that: first undo the subtraction, then undo the multiplication.

What you did was equivalent to first subtracting 2 from 4, which is not what PEMDAS says to do in evaluating. At that point, you are not yet solving (undoing).

It will be helpful, though, to see that subtraction is the same as adding the negative, so my equation is really

10 = 4 + (-2) x
​

To solve this, first subtract 4 from both sides, leaving

6 = (-2)x
​

Then divide by -2:

-3 = x
​

Do you see the difference from what you did?

 

[JeffM]

I am following a video on Khan Academy showing me how to use the law of cosine to find an angle. I filled it in and I have this. 400=6,100-6,000 x COS(?)

My first instinct is to use reverse pemdos to simplify it. 400=100 X COS(?)
And then divide by 100 on both sides to finally get 4 = COS(?)

But in the video they start by subtracting 6,100 to get -5,700 = -6000 X COS(?)
Then they divide by -6000 to end up with. 57/60 = COS (?)
Finally they subtract COS to end up with. COS-1(19/20) = ?
And the answer is 18.19

I know this answer is correct but they seem to be simplifying out of order and I can not understand what I was doing wrong. Could some please explain. Thanks so much!

$\displaystyle \text {Let } x = cos ( \theta ).$

$\displaystyle \therefore 400 = 6100 - 6000 * cos ( \theta ) \implies 400 = 6000 - 6000x.$

How would you solve for x?