Question
Examples
Find all angles, $0^{\circ} \leq A< 360^{\circ}$, that satisfy the equation below, to the nearest tenth of a degree (if necessary).
\[
\tan A-3=3 \tan A-6
\]
Answer
Rounding to the nearest tenth of a degree, we find that the angles that satisfy the equation are \( A = \boxed{56.3^{\circ}} \) and \( A = \boxed{236.3^{\circ}} \).
Step 1 ：The given equation is a simple linear equation in terms of \( \tan A \). We can solve it by first simplifying the equation and then finding the value of \( A \) by taking the inverse tangent of the solution. However, since the tangent function has a period of \( 180^{\circ} \), we need to add \( 180^{\circ} \) to the solution to find all possible angles in the range \( 0^{\circ} \leq A<360^{\circ} \).
Step 2 ：By solving the equation, we find that \( A1 = 56.309932474020215 \) and \( A2 = 236.30993247402023 \).
Step 3 ：Rounding to the nearest tenth of a degree, we find that the angles that satisfy the equation are \( A = \boxed{56.3^{\circ}} \) and \( A = \boxed{236.3^{\circ}} \).
