Solve the equation:

\[
\sin(x + 80^\circ) = 0.6
\]

for \(-180^\circ < x < 180^\circ\).

Answer: \(x = -86.26^\circ\) or \(x = 126.26^\circ\).

Forgive me, but those two answers are not correct.
You have no way to operate directly with the nuts and bolts of the sine function. You have to use a table and look it up.
To start, look up the angle that has its sine = 0.6 .
That's 37.87° degrees and 143.13° Wonderful. Now we know that (x + 80°) = 37.87° and (x + 80°) = 143.13°
Take each equation and subtract 80° from the left side of it, and you wind up with
x = -42.13° and x = 63.13°
What part of this is complicated or confusing ?

Answered by AL2006 | 2024-06-10

The solutions to the equation sin ( x + 8 0 ∘ ) = 0.6 are approximately x ≈ − 43.1 3 ∘ and x ≈ 63.1 3 ∘ , both of which are in the specified range of − 18 0 ∘ < x < 18 0 ∘ .
;

Answered by AL2006 | 2024-12-24