How do you evaluate tan (pi/12) using the half angle formula?
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Question “How do you evaluate tan (pi/12) using the half angle formula?”
How do you evaluate tan (pi/12) using the half angle formula?
Answer
2 – sqrt3
Explanation:
Use the trig identification: tan 2a = (2tan a)/(1 – tan^2 a)
Trig table –->
tan 2a = tan (pi/6) = 1/sqrt3
We get:
1/sqrt3 = (2t)/(1 – t^2).
Cross multiply –>
(1-t2) = 2sqrt3
t^2 + 2sqr3t – 1 = 0
This quadratic equation can be solved for t.
D = d2 + 4ac = 3(3) + 4 = 16
–> d = +-4
There are two real roots to this:
t = tan (pi/12) = -b/(2a) +- d/(2a) = -(2sqrt3)/2 +- 4/2 = – sqrt3 +- 2
.
Since tan (pi/12)
Positive, therefore,
tan (pi/12) = 2 – sqrt3
Calculator
tan (pi/12) = tan 15^@ = 0.27
2 – sqrt3 = 2 – 1.73 = 0.27
. OK
Conclusion
Above is the solution for “How do you evaluate tan (pi/12) using the half angle formula?“. We hope that you find a good answer and gain the knowledge about this topic of trigonometry.
