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What are the solutions for this trig equation?

0 votes

interval:(0, 2pi) 

cosx/3-sinx/3=0 

asked Nov 17, 2014 in TRIGONOMETRY by anonymous

1 Answer

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The trigonometric equation cos(x/3) - sin(x/3) = 0

cos(x/3) = sin(x/3)

1 = sin(x/3)/cos(x/3)

tan(x/3) = 1

Let x/3 = t

tan(t) = tan(π/4)

The general solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

θ = t, α = π/4

For n = 0, t = (0)π + π/4 = π/4

x/3 = t x = 3t = 3π/4

For n = 1, t = (1)π + π/4 = 5π/4

x/3 = t x =3t = 1/4

The solutions are in the interval (0, 2pi) is 3π/4.

answered Nov 17, 2014 by david Expert
edited Nov 17, 2014 by david

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