assignment 7.5: solving trigonometric equations\nscore: 40/100 answered: 4/10\nquestion 5\nsolve \\( \\sin…

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

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

Answer

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)