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8 votes
8 votes
Tan(3x/7 - π/5)= -√3/3

User Stefaan Colman
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1 Answer

24 votes
24 votes

Answer:

x is 7·π/30

Explanation:

The given equation is presented as follows;

tan(3·x/7 - π/5) = (-√3)/3

We have that arctan (√3)/3 = π/6, and tangent of an angle is negative in the second quadrant, we get;

arctan (-√3)/3 = -π/6 = 5·π/6

∴ tan(-π/6) = -√3/3 = tan(3·x/7 - π/5)

-π/6 = 3·x/7 - π/5

x = (-π/6 + π/5) × 7/3 = (6·π - 5·π)/30 × 7/3 = π/30 × 7/3 = 7·π/30

x = 7·π/30

User Kstubs
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3.0k points