Answer:
[tex]a=4.4\degree[/tex] and [tex]b=31.60\degree[/tex]
Step-by-step explanation:
The given trigonometric equation is:
[tex]8\sin (5x)=3[/tex]
Divide both sides by 8;
[tex]\sin (5x)=\frac{3}{8}[/tex]
Take sine inverse of both sides.
[tex]5x=\sin^{-1} (\frac{3}{8})[/tex].... in the first quadrant.
[tex]5x=22.02\degree[/tex]
Divide through by 5
[tex]x=4.4\degree[/tex]
[tex]5x=180\degree- \sin^{-1} (\frac{3}{8})[/tex].... in the second quadrant.
[tex]5x=180\degree-22.02\degree[/tex]
[tex]5x=157.98\degree[/tex]
[tex]x=31.60\degree[/tex]
Therefore [tex]a=4.4\degree[/tex] and [tex]b=31.60\degree[/tex]
