Question

Trigonometric equations

5sinx = 3sinx + square root of 2

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}♪`

Let's solve for x ~

`\qquad \sf  \dashrightarrow \:5 \sin(x) = 3 \sin(x) + √(2)`

`\qquad \sf  \dashrightarrow \:5 \sin(x) - 3 \sin(x) = √(2)`

`\qquad \sf  \dashrightarrow \:2 \sin(x) = √(2)`

`\qquad \sf  \dashrightarrow \: \sin(x) = √(2) / 2`

`\qquad \sf  \dashrightarrow \: \sin(x) = (1)/( √(2) )`

`\qquad \sf  \dashrightarrow \:x = 45 \degree \: \: or \: \: (\pi)/(4) \: rad`

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