How do you find the reference angle for #(theta) = (6pi) / 7#?
2 Answers
Okay, first of all, the problem lies in the format we can see the angle in. It seems to be in radians as it is using measures of
There's a short way to do it and a long way to do it; I'll explain both.
Let's say we were converting an angle of 50° to radians, using measures of
If at any point you want another example on doing this, check here.
I'll start with the long version first:
So you can use this little formula:
Your case is stated after I explain this method forwards.
All you have to do is substitute it in and then simplify:
So we could do the same process to go from radians to degrees:
All we have to do is substitute in the number of radians we want to convert (in this case we'll use the answer we got in our last conversion [0.087])
In your case, to get the number of radians, just simplify what you have e.g
Then manipulate it to find
The shorter method may seem more simple:
We know that for every
So, in your case, we have
Now, if
Now simply multiply it in whichever method you wish:
Now that we have dealt with the format and put it into degrees - it's easy to use:
To figure out which quadrant it is in (i.e. which formula to use), we need to imagine the quadrants:
When we figure out which quadrant our angle (154.286°) is in, we can decide which formula to use.
As 150.286° is between 90° and 180°, it is in the second quadrant , where we use
Finally,
The reference angle is
