SOLUTION: find the exact value of tan(-3 pie)

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Question 149789: find the exact value of tan(-3 pie)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28-3pi%29


-tan%283pi%29 Use the identity tan%28-u%29=-tan%28u%29 to rewrite the expression.


-sin%283pi%29%2Fcos%283pi%29 Rewrite tangent in terms of sine and cosine.


-sin%282pi%2Bpi%29%2Fcos%282pi%2Bpi%29 Rewrite 3pi as 2pi%2Bpi


Rewrite the expression using the identities sin%28A%2BB%29=sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29 and cos%28A%2BB%29=cos%28A%29cos%28B%29-sin%28A%29sin%28B%29


Now, let's reference the unit circle




From the unit circle, we can see that at the angle pi, there is a point on the unit circle . So this tells us that cos%28pi%29=-1 and sin%28pi%29=0. Also at the angle 2pi, there is a point on the unit circle . So this tells us that cos%282pi%29=1 and sin%282pi%29=0.

-%28%280%29%28-1%29%2B%281%29%280%29%29%2F%28%281%29%28-1%29-%280%29%280%29%29 Take the cosine of pi to get -1. Take the sine of pi to get 0. Take the cosine of 2pi to get 1. Take the sine of 2pi to get 0.


-%280%2B0%29%2F%28-1%2B0%29 Multiply


-%280%29%2F%28-1%29 Add


0 Reduce


So tan%28-3pi%29=0