Looking for help with solving these types of problems. It's not homework, I'm not in school. I'm not asking for specific answers I just really want to know how to solve these types of problems. Inb4 Google, tried it, the explanations are NOT showing me how they get to the answer. I'm retarded obviously, please help. Thanks.
>It's not homework, I'm not in school.
Moshi moshi, baito-desu.
Brainlets; when will they learn?
>>7964381
I have a master's degree dude, but not in math. I have no grades to worry about. Didn't ask for answers. Asked for how does one solve these TYPES of problems. Is it really that fucking hard to believe? The fuck.
>>7964384
does your mom know you're on the internet?
Okay, take a look at pic related...
You want to find the value of x for which the cosine of x is -0.78 in the range where x is between 0 and 2*pi.
By observation, you see that there are two values of x for which this is true and that these two values are symmetric around x = pi
Start by finding the arc cosine of -0.78
Take a scientific calculator, enter -0.78
If you are using calc.exe in windows under the View -> Scientific option, you will see a checkbox labelled "Inv", for inverse. Check that box.
Select the radio button marked Radians. We do this because the range was from 0 to 2*pi. If the range was given as 0 to 360 degrees, we would have selected Degrees
Then click the button labelled 'cos', which is short for cosine.
The result given is x = 2.46546, etc.
This is the first value of x in radians for which the cosine = -0.78
To find the second value, find the value pi - the first value of x and add that value to pi.
pi - x + pi, or 2*pi -x
Which in this case is 2*pi - 2.46546, etc.
x = approximately 3.8177
I hope this helps!
>>7964498
I might be belaboring the obvious, but the Inv cos sequence returns the arc cosine - the inverse cosine, if you like, of -0.78 in this example above.
If you enter 2.46546, etc. and then click cos, that is equivalent to:
cos(2.46546, etc) which will give a value as close to -0.78 as you enter more of the numbers past the decimal point.
>>7964363
The interval being states in terms of pi means its in radians
Convert the radians to degrees and it will be more intuitive
2pi = 360 degrees
So you want the degree X such that cos(x) = -0.78
Look at the UNIT CIRCLE
You know that cos is negative between 90 and 270 degrees so that gives you a range
You know that in this range, cos will equal -0.78 twice, because the range covers two quadrants (the top left and bottom left)
Solving for X with a calculator gives you 141 degrees
You know this is in the top left quadrant
If you mirror this around the X axis, you will get the angle in the bottom left quadrant
To do this, just find the difference between X and 180, then add that difference to 180 (since the x axis is 180 degrees)
Now you have your two solutions, convert both back to radians
>>7965017
2016
Using degrees
>>7964363
pi and 2pi, since those are the only (cutie)pies in there. And if your x is not a cutiepie then you should question your judgement.
