Question 1101887: Find two negative angles that are coterminal with θ. Answers may vary.
0 = π/2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your angle is pi/2.
all angles that are coterminous to this angle will be either 2 * pi degrees more than it or 2 * pi degrees less than it.
since 2 * pi is equal to 4 * pi / 2, then:
pi/2 minus 4 * pi/2 is equal to -3 * pi/2.
-3 * pi/2 minus 4 * pi/2 is equal to -7 * pi/2.
two negative angles coterminous with pi/2 would be -3pi/2 and -7pi/2
you can go on forever.
every angle that is 4pi/2 less than the previous angle will be coterminous with pi/2.
in degrees, every angle that is 360 degrees less than the angle will be coterminous with the angle.
pi/2 radians is equal to 90 degrees.
subtract 360 from that and the first negative coterminous angle would be 90 - 360 = -270.
subtract 360 from -270 and the next negative coterminous angle would be -270 - 360 = -630 degrees.
to convert degrees to radians, multiply the angle in degrees by pi / 180 and you will get the equivalent angle in radians.
90 degrees * pi / 180 is equal to pi/2 radians.
-270 degrees * pi/180 is equal to -3pi/2 radians.
-630 degrees * pi/280 is equal to -7pi/2 radians.
looking at the unit circles, it would look like this.
an angle of pi/2 radians is the vertical line going up on the graph.
subtract 2pi from that and the coterminous angle is equal to -3pi/2.
subtract 4pi/2 from that and the coterminous angle is equal to -7pi/2.
subtract 4pi/2 from that and the coterminous angle is equal to -11pi/2.
this can go on forever.
more coterminous angles are 4pi/2 radians less than the previous angle.
you go to -15pi/2, -19pi/2, -23pi/2, ..... forever.
all of these angles are coterminous with pi/2.
the actual formula would be:
coterminous angle to pi/2 = pi/2 plus or minus n * 2pi, where n is a positive integer.
this can also be written as:
coterminous angle to pi/2 = pi/2 plus or minus n * 4pi/2, where n is a positive integer.
-3pi/2 is equal to pi/2 minus 1 * 4pi/2.
-7pi/2 is equal to pi/2 minus 2 * 4pi/2.
-11pi/2 is equal to pi/2 minus 3 * 4pi/2.
etc .....
in degrees, the coterminous angle to 90 is equal to 90 plus or minus n * 360.
-270 is equal to 90 minus 1 * 360.
-630 is equal to 90 minus 2 * 360.
-990 is equal to 90 minus 3 * 360.
etc ...
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