SOLUTION: Hey. {{{tan (195)}}} I got figured it would be something with {{{pi+pi/4-pi/6}}} but I am unsure how to go based on the sum and difference identities.

Algebra ->  Trigonometry-basics -> SOLUTION: Hey. {{{tan (195)}}} I got figured it would be something with {{{pi+pi/4-pi/6}}} but I am unsure how to go based on the sum and difference identities.       Log On


   

Question 1054319: Hey. tan+%28195%29
I got figured it would be something with pi%2Bpi%2F4-pi%2F6 but I am unsure how to go based on the sum and difference identities.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
I tried splitting this in various ways and found this path:
195=60%2B3%2A45=60%2B45%2B90=45%2B150, using degree measures instead of as radians, just because this was easier than dealing with fractional formed numbers.

Check on the Unit Circle where you find 150 degrees. This is 30 degrees short of 180 degrees. Identify sine and cosine for 150 degrees. Form Tangent value of 150 degrees from these.
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tan%28150%29=%281%2F2%29%2F%28-sqrt%283%29%2F2%29, and of course, simplify this before going further.

Now you would be dealing with tan%28195%29=tan%2845%2B150%29 and you can find the identity to use for this tangent function, the angle addition formula for tangent.

Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hey. tan+%28195%29
I got figured it would be something with pi%2Bpi%2F4-pi%2F6 but I am unsure how to go based on the sum and difference identities.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

tan(195°) = tan(15°) = tan%2845%5Eo-30%5E0%29 = 2 - sqrt(3).


By the way, ignore writing by "josgarithmetic".
It is wrong.