The Law of Sines
The Law of Sines – Example 2: \(75+42+x=180→ 117+x=180→x=180-117=63 ^\circ \) To find sides use the law of sines: \(\frac {a}{sin\ A}=\frac {b}{sin\ B}=\frac {c}{sin\ C}\) \(\frac {22}{sin\ 75}=\frac {b}{sin\ 42}= \frac {c}{sin\ 63}\) Now, use proportional ratios: \(\frac {a}{b}=\frac{c}{d} → a×d=c×b\) \(\frac {22}{sin\ 75}=\frac {b}{sin\ 42} → b=\frac {22 × sin\ 42 } {sin\ […]
How to Verify Inverse Functions by Composition?
TL;DR: Think of two functions as a door and a key — if one really undoes the other, plugging one into the other should land you right back at x. That’s the test for inverses: f(g(x)) must equal x AND g(f(x)) must equal x for every valid input. One direction isn’t enough — you have […]
