Question

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

Answer 1

Answer:

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

Step-by-step 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.