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Sin θ − 4 = 8 sin θ?

0 votes

Solve for all degree solutions and if 0° ≤ θ < 360°.

asked Dec 8, 2014 in TRIGONOMETRY by anonymous

1 Answer

0 votes

 

The trigonometric equation is sin θ - 4 = 8sin θ.

Subtract 8sin θ from each side.

sin θ - 4 - 8sin θ = 0

- 7sin θ - 4 = 0

Add 4 to each side.

- 7sin θ = 4

Divide each side by negative 7.

sin θ = - 4/7.

sin θ = sin[sin- 1(- 4/7)]

sin θ = sin[- 34.850].

The genaral solution of sin(θ) = sin(α) is θ = nπ + (- 1)nα, where n is an integer.

⇒ θ = nπ + (- 1)n(- 34.850)

If n = 0, θ = (0)π + (- 1)0(- 34.850) = - 34.850.

If n = 1, θ = (1)π + (- 1)1(- 34.850) =1800 + (- 1)1(- 34.850) = 1800 + 34.850 = 214.840

If n = 2, θ = (2)π + (- 1)2(- 34.850) =3600 - 34.850 = 325.150.

The solutions of the given equation are θ = 214.840 and θ = 325.150 in the interval [00, 3600).

answered Dec 8, 2014 by lilly Expert

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