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Question

1. If sin(x+40⁰)=1/2, where 90⁰<x<180⁰, what is the value of x

Answer 1

If you take the inverse sin of both sides of the equation then it becomes

x + 30° = sin^-1 (1/2)

The inverse sin of 1/2 = 30° or 150°. Since we're told to look in quadrant II (90° < x 180°), we know that it must be 150°. Now are equation is

x + 30° = 150°

And you can solve for x from there.