SOLUTION: I need help finding the exact value of tan 585 degrees?

Question 942817: I need help finding the exact value of tan 585 degrees?

Found 3 solutions by Alan3354, Fombitz, Theo:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
You can use a calculator.
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
If you don't have a calculator, you can always type into google.
.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
tan(585) = 1
the easy way to find this is to put tan(585) in your calculator and it will tell you that the tangent of 585 is equal to 1.
the way they want you to find it manually is as follows:
start with 585 degrees.
subtract 360 to get 225 degrees.
since the angle is now positive between 0 and 360 degrees, find the quadrant that the angle is in and then apply the rules for that quadrant to get the reference angle.
the angle is in quadrant 3 because it is between 180 degrees and 270 degrees.
the reference angle for an angle in quadrant 3 is found by subtracting 180 from that angle.
225 - 180 = 45 degrees.
45 degrees is the reference angle.
you know, or should know, that sine of 45 degrees is equal to sqrt(2)/2.
you know, or should know, that cosine of 45 degrees is also equal to sqrt(2)/2.
that would be in the first quadrant.
in the third quadrant sine is negative and cosine is negative.
that makes sine of 225 degrees equal to -sqrt(2)/2.
that makes cosine of 225 degrees equal to -sqrt(2)/2.
tangent of 225 degrees is equal to sine of 225 degrees / cosine of 225 degrees.
tangent of 225 degrees is equal to -sqrt(2)/2 divided by -sqrt(2)/2 which makes tangent of 225 degrees equal to 1.
since 585 degrees is exactly 360 degrees more than 225 degrees, it is in exactly the same position on the unit circle as 225 degrees and therefore has the same trigonometric function values as 225 degrees.
tangent of 585 degrees is therefore equal to 1.
the calculator confirms it.

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