Solve the equation?

Solve

tanx-sqrt3=0
,
xin(-pi,-pi/2)uu(-pi/2,pi/2)uu(pi/2,pi)

2 Answers
Alan P.
Apr 9, 2018

x=pi/3 or x=-(2pi)/3

Explanation:

tan(x)-sqrt(3)=0
color(white)("XXX")rarr tan(x)=sqrt(3)

In Quadrant I, this is one of the standard triangles:
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Using the CAST notation for the Quadrants, a reference angle in Quadrant III will have the same tan(x) value i.e. (-pi+pi/3) will have the same value.
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Nghi N
Apr 9, 2018

x = pi/3 + kpi

Explanation:

tan x = sqrt3
Trig table and unit circle give 2 solutions:
x = pi/3 and x = pi/3 + pi = (4pi)/3
General answer:
x = pi/3 + kpi
Inside the interval (-pi, -pi/2), the answer is (4pi)/3
Inside the interval (- pi/2, pi/2), the answer is (pi/3)
No answer in the interval (pi/2, pi)

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