Math
posted by Juan on .
What are the steps to getting the tan of 345degree, without the use of a calculator?

345°=360°15°
tan(AB)=(tan A  tan B)/(1  (tan A)*(tan B))
tan(360°)=0
tan(360°15°)= tan(360°)tan(15°)/(1(tan(360°)*(tan(15°))
tan(360°15°)= 0tan(15°)/(10*(tan(15°))
tan(360°15°)=tan(345°)= tan(15°)/(10)
tan(345°)= tan(15°)/1
tan(345°)= tan(15°) 
tan(x/2) = [1  cos(x)]/sin(x)
tan(30°/2)=tan(15°)
sin(30°)= 1/2
cos(30°)= sqroot(3)/2
tan(30°/2)=tan(15°)= [1  cos(30°)]/sin(30°)
= (1  sqroot(3)/2)/(1/2)
= 2  sqroot(3)
tan(15°) = 2  sqroot(3)
tan(345°)= tan(15°)
tan(345°)= (2  sqroot(3))
tan(345°)= sqroot(3)2 
or ...
345° is coterminal with 15°
so tan 345° =  tan15
=  tan(4530)
=  (tan45  tan30)/(1 + tan45tan30)
= (11/√3)/(1+1/√3) , multiply top and bottom by √3
= (1  √3)(√3 + 1)
You can rationalize if necessary to get Bosnian's answer