Question 428071: State the quadrant of the angle theeta and find the value of the basic angle if
a) theeta = 250 degrees,
b) theeta = 390 degrees,
c) theeta = -60 degrees,
d) theeta = -100 degrees.
:)
Found 2 solutions by shree840, Theo:
Answer by shree840(260)   (Show Source):
You can put this solution on YOUR website! four quadrant each has 90 degrees
a 250= 180+70 third quad
b 390=360+30 first quad
c-60=300= 270+30 third quad
d -100=260=180+80=third quad
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! if the angle is 250 degrees, then the angle is in the third quadrant and the reference angle is 250 - 180 = 70 degrees.
if the angle is 390 degrees, then the angle is in the first quadrant and the reference angle is 30 degrees.
if the angle is -60 degrees, then the angle is in the fourth quadrant and the reference angle is 60 degrees.
if the angle is -100 degrees, then the angle is in the third quadrant and the reference angle is 80 degrees.
the reference angle is a positive acute angle that is less than 90 degrees.
this is also called the base angle.
when your angle is in the first quadrant, your reference angle is the angle.
when your angle is in the second quadrant, your reference angle is 180 degrees minus the angle.
when your angle is in the third quadrant, your reference angle is the angle minus 180 degrees.
when your angle is in the fourth quadrant, your reference angle is 360 minus the angle.
all this assumes that your angle is a positive angle.
when your angle is a negative angle, you can convert it to a positive angle and use the positive angle rules.
you convert a negative angle to a positive angle by adding 360 to it until it becomes positive.
let's go through your exercise using the rules.
your first angle is 250 degrees.
this is in the third quadrant.
in the third quadrant, the reference angle is the angle minus 180 degrees.
this equals 250 - 180 = 70 degrees.
your second angle is 390 degrees.
since this is greater than 360 degrees, we subtract 360 from it until we get a positive angle less than 360 degrees.
390 - 360 = 30 degrees.
this is a positive angle in the first quadrant.
since this angle is in the first quadrant, the reference angle is the angle which is 30 degrees.
your third angle is -60 degrees.
since this angle is negative, we add 360 to it until we get a positive angle less than 360 degrees.
-60 + 360 = 300 degrees.
300 degrees is in the fourth quadrant, so he reference angle is 360 - 300 = 60 degrees.
your fourth angle is -100 degrees.
since this angle is negative, we add 360 to it until we get a positive angle less than 360 degrees.
-100 + 360 = 260 degrees.
260 degrees is in the third quadrant so the reference angle is 260 - 180 = 80 degrees.
you might be interested in a lesson i wrote on angles shown below.
enjoy.
if you have questions regarding any of the material, let me know and i'll answer them as best i can.
http://www.algebra.com/algebra/homework/playground/THEO-20091204.lesson
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