How to find the exact value of tan(-pi/12)?

Samara Goodman

Samara Goodman

Answered question

2023-03-24

How to find the exact value of tan(-π/12)?

Answer & Explanation

Joselyn Arias

Joselyn Arias

Beginner2023-03-25Added 5 answers

Identify the precise value of tan ( - π 12 )
Answer: ( 3 - 2 )
Explanation:
Call tan ( - π 12 ) = tan x .
tan 2 x = tan ( - 2 π 12 ) = - tan ( π 6 ) = - 3 3 = - 1 3
Put the trig identity to use: tan 2 x = 2 tan x 1 - tan 2 x , we get:
- 1 3 = 2 tan x 1 - tan 2 x . Cross multiply:
tan 2 x - 1 = 2 3 tan x .
The quadratic equation must be solved.
tan 2 x - 2 3 tan x - 1 = 0
D = d 2 = b 2 - 4 a c = 12 + 4 = 16 ---> d = ± 4
tan x = 2 3 2 ± 4 2 = 3 ± 2 .
Since the arc ( - π 12 ) is in Quadrant IV, its tan is negative, then:
tan x = tan ( - π 12 ) = 3 - 2 .
Check by calculator.
tan ( - π 12 ) = tan ( - 15 ) = - 0.27 .
( 3 - 2 ) = ( 1.73 - 2 ) = - 0.27 .

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