SOLUTION: Express the sin (-140�) as a function of a positive acute angle 1) sin 40� 2) tan 40� 3) -sin 40� 4) -tan 40�

Question 858028: Express the sin (-140�) as a function of a positive acute angle
1) sin 40�
2) tan 40�
3) -sin 40�
4) -tan 40�
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Express the sin (-140�) as a function of a positive acute angle
-----
quadrant: QIII where sin is negative.
Angle:: 360-140 = 220
Reference Angle:: 220 = 180+40
RA = 40 degrees
--------------------
sin(-140) = -sin(40)
=================
Cheers,
Stan H.
1) sin 40�
2) tan 40�
3) -sin 40�
4) -tan 40�

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
-140 degrees is in the third quadrant.
to turn that into a positive angle, add 360 to it to get:
-140 degrees + 360 degrees is equal to 220 degrees.
-140 degrees is equivalent to 220 degrees.
to find the reference angle for 220 degrees, you would use the following formula:
180 + x = 220
solve for x to get:
x = 220 - 180 which results in:
x = 40 degrees.
the sine is positive in the first quadrant but negative in the third quadrant.
so the sin (-140) degrees is equal to the sin (220) degrees which is equal - the sine of (40) degrees.
to confirm this is correct, use your calculator to find the sine of (220) degrees) and the sine of (-140) degrees and the sine of (40) degrees.
you will find that the sin of (220) and (-140) degrees is the same and that both of them are equal to - sine of (40) degrees.
the numbers from my calculator are:
sin(220) = -.64278676097
sin(-140) = -.6427876097
sin(40) = .6427876097
a picture of what the angle looks like is shown below:

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