Question 1040117: Need some help drawing and labeling an example of an angle with negative measure in standard position. Then create an angle with a positive measure that is coterminal with this angle.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let's say your angle is -90 degrees.
add 360 to it and the equivalent positive angle is 270 degrees.
any time you add or subtract 360 degrees from any angle, you get an equivalent angle that is coterminous with that angle.
if your angle is negative, just keep adding 360 to it until it becomes positive.
if your angle is positive and you want to get the negative equivalent, just keep subtracting 360 from it until it becomes negative.
the unit circle is used to demonstrate angles and their equivalents in different quadrants.
an angle in a different quadrant is equivalent if it has the same values for each of the trigonometric functions.
for example, using -90 as the angle, it's equivalent positive angle would be 270 degrees.
the position of 270 degrees in the unit circle is the same position as -90 degrees in the unit circle.
to get to -90 degrees from 0 degrees, you would rotate the angle clockwise until you reach -90 degrees.
to get to 270 degrees from 0 degrees, you would rotate the angle counter-clockwise until you reach 270 degrees.
every time you add 360 degrees to an angle, you are rotating the angle counter-clockwise 360 degrees.
every time you subtract 360 degrees from an angle, you are rotating the angle clockwise 360 degrees.
here's a picture of the unit circle.
the angle used in the example is -90 degrees.
add 360 to that and you get the equivalent angle of +270 degrees.
those angles occupy the same position on the unit circle.
they are equivalent.
equivalent means the value of all their trig functions is the same.
you can confirm by using your calculator.
sin(-90) = -1
sin(270) = -1
cos(-90) = 0
cos(270) = 0
since tan = sin/cos, if sin is the same and cos is the same, then tan will be the same.
just to confirm:
tan(-90) = undefined
tan(270) = undefined
similarly, if sin is the same, then csc will be the same because csc is equal to 1/sin.
similarly, if cos is the same, then sec will be the same because sec is equal to 1/cos.
just to confirm:
csc(-90) = -1
css(270) = -1
sec(-90) = undefined
sec(270) = undefined
a value of undefined is caused by a division by 0.
what this says is that you only really need to check sine or cosine.
if they are the same, then the rest of the trig functions will be the same because those functions are derived from sine and cosine.
tan = sin/cos
cot = cos/sin
csc = 1/sin
sec = 1/cos
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