SOLUTION: Tan 195 degrees

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Question 625300: Tan 195 degrees
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
I assume that the instructions for the problem say to find the exact value. Otherwise we could just use our calculators and it wouldn't be much of a problem. (Please include the instructions so we don't have to guess.)

Whenever the expression "exact value" is used in Trig. it is cods for "use special angles". 195 has a reference angle of 15 which is not a special angle. So 195 itself is not a special angle (which would have made this problem easy).

Now we have to find a way to express 195 in terms of special angles. We have to ask ourselves:If you're lucky, you will be able to answer "yes" to one of the first three questions. That is because we have formulas for sums, differences and halves of angles.

With a little effort we should be able to answer "yes" to the first two equations:
195 = 150 + 45
and
195 = 240 - 45
So we will be able to get an answer in two ways:
tan(195)
tan(150+45)
Using the formula we get:

We should be able to find these tan's easily since they are all special angles:

which simplifies as follows:

Multiplying the numerator and denominator by 3:

Rationalizing the denominator:









Another solution using 240 - 45:
tan(195)
tan(240-45)
Using



Rationalizing the denoinator:








So either way we find that the exact value of tan(195) is .
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