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Find all solutions of the equation. 5 sin x − 82√ = 3 sin x − 72√

User Mikdore
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1 Answer

4 votes

Answer:

  • x = arcsin(√20.5 -3√2) +2kπ . . . k any integer
  • x = π - arcsin(√20.5 -3√2) +2kπ . . . k any integer

Explanation:

Add √(82) -3sin(x) to both sides to get ...

2sin(x) = √82 -√72

Now, divide by 2 and find the arcsine:

sin(x) = (√82 -√72)/2

x = arcsin((√82 -√72)/2)

Of course, the supplement of this angle is also a solution, along with all the aliases of these angles.

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In degrees, the solutions are approximately 16.562° and 163.438° and integer multiples of 360° added to these.

User Basim Sherif
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