Question
Asked Jun 11, 2019
Give a general formula for all the solutions.
2 sin 0-53 sin 0
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Give a general formula for all the solutions. 2 sin 0-53 sin 0

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Expert Answer

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Step 1
The given trigonometric equation is 2 sin 0-5
-3 sin 0
Let u sin and simplify the given equation as follows
( sin0u)
2и - 5 %3D - Зи
2и + Зи 3 5
5u 5
5
u=-
5
u=1
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The given trigonometric equation is 2 sin 0-5 -3 sin 0 Let u sin and simplify the given equation as follows ( sin0u) 2и - 5 %3D - Зи 2и + Зи 3 5 5u 5 5 u=- 5 u=1

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Step 2
Substitute u sin 0 to obtain the solution
(u-sin
sin 1
sin 0 sin
sin
2
It is known that, the solutions ofthe equation sin 0= sin a are 0 2n7 + a
Thus, the solutions ofthe given equation is 0= 2nn +
=
2
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Substitute u sin 0 to obtain the solution (u-sin sin 1 sin 0 sin sin 2 It is known that, the solutions ofthe equation sin 0= sin a are 0 2n7 + a Thus, the solutions ofthe given equation is 0= 2nn + = 2

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