Question

assignment 7.5: solving trigonometric equations
score: 40/100 answered: 4/10
question 5
solve \\( \sin (x)=0.46 \\) on \\( 0 \leq x<2 \pi \\).
there are two solutions, \\( a \\) and \\( b \\), with \\( a\\( a= \\)
\\( b= \\)
give your answers accurate to 3 decimal places.
question help: video \\( \square \\) post to forum

Explanation:

Step1: Find the principal solution

Use the inverse - sine function \(x = \sin^{-1}(0.46)\).
Using a calculator, \(x=\sin^{-1}(0.46)\approx0.480\) (rounded to 3 decimal places). This is the solution in the first - quadrant (\(0\leq x\leq\frac{\pi}{2}\)).

Step2: Find the second solution

Since \(\sin(x)=\sin(\pi - x)\), the second solution \(B\) in the interval \(0\leq x\lt2\pi\) is \(x=\pi-\sin^{-1}(0.46)\).
\(x=\pi - 0.480\approx3.142-0.480 = 2.662\) (rounded to 3 decimal places).

Answer:

\(A = 0.480\)
\(B=2.662\)