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Sum and Difference Formulas - Printable Version

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Sum and Difference Formulas - Dreamer567 - 03-10-2010 10:30 AM

Hello, another math question here. Can someone show me step by step how to do this problem please?

Evaluate using the appropriate sum, difference, or double angle formula: Tan 165 Degrees

I have a test tomorrow, so any help would be greatly appreciated. Thanks.


Re: Sum and Difference Formulas - magikarp - 03-10-2010 11:45 AM

I'm not sure I understand the way you're supposed to do this, but I'll go ahead and give one way to answer it anyway. Hopefully it's helpful.

It would be easier to do this question if the angle were smaller, because you probably only know the exact values of tan(60), tan(30), tan(45), and tan(0). Now, since the tangent function has a period of 180 degrees, you can either add or subtract any multiple of 180 degrees from the angle and still get the same result.

tan(165) = tan(165-180) = tan(-15)

At this point you can use the difference formula to find tan(45-30), but I think it's easier to simplify more first.

tan(-x) = -tan(x), so tan(-15) = -tan(15)

Now you use the difference formula.

tan(u-v) = (tan(u) - tan(v)) / (1 + tan(u)tan(v))
-tan(15)=-(tan(45) - tan(30)) / (1 + tan(45)tan(30))
=-( 1 - (1/sqrt(3)) / (1 + (1/sqrt(3))
=-(3 - sqrt(3)) / (3 + sqrt(3))