SOLUTION: Use an addition or subtraction formula to find the exact value of the expression.
Tan(-5pie/12)
The formula is tan(s-t)=tan s + tan t/ 1+tans tant
or
tan(s+t)= tan s-tan t
Algebra.Com
Question 277603: Use an addition or subtraction formula to find the exact value of the expression.
Tan(-5pie/12)
The formula is tan(s-t)=tan s + tan t/ 1+tans tant
or
tan(s+t)= tan s-tan t/ 1+tans tant
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
Try:
To make this more natural, remember that the primitive tangent function has period of pi. So we have Tan(-5pi/12) congruent to Tan(7pi/12) mod pi.
Now: What functions do we easily know the value to for trigonometrics? pi/3 is certainly one. So, pi/3=4pi/12---> We need to know 3pi/12=pi/4 ! This is also an easy find.
So, we take Tan(7pi/12)=Tan(3pi/12 + 4pi/12) Now we use your formulae:
Tan(3pi/12 + 4pi/12)=[Tan(pi/4)-Tan(pi/3)]/(1+Tan(pi/4)Tan(pi/3))
Now it remains to remember what Tan(pi/4) and Tan(pi/3) are. We use the definition of Tangent.
Tan(x)=Sin(x)/Cos(x).
So Tan(pi/4)=1.
Tan(pi/3)=(sqrt(3)/2)/(1/2)=sqrt(3)
Finally, substitute into our expression:
(1-sqrt(3))/(1+sqrt(3))
Now, simplify:
==
This could be done quicker, but I hope you can see the full details of what is going on through this procedure.
RELATED QUESTIONS
Use an addition or subtraction formula to find the exact value of the expression.... (answered by robertb)
Use an Addition or Subtraction Formula to find the exact value of the expression.
tan... (answered by lynnlo)
Use an Addition or Subtraction Formula to find the exact value of the expression.
tan... (answered by lynnlo)
tan (-5pi/12)
Use an Addition or Subtraction Formula to find the exact value of the... (answered by lwsshak3)
Use an Addition or Subtraction Formula to write the expression as a trigonometric... (answered by Alan3354)
Use an Addition or Subtraction Formula to find the exact value of the expression, as... (answered by lwsshak3)
Use an Addition or Subtraction Formula to write the expression as a trigonometric... (answered by lwsshak3)
Addition or subtraction formula to find the exact value... (answered by lwsshak3)
Use an Addition or Subtraction Formula to write the expression as a trigonometric... (answered by lwsshak3)