Using Identities
Now that we have tackled basic equations, let's consider equations that might involve our trigonometric identities. We can follow the previous outline by modifying step #1.
- Use trigonometric identities and algebraic techniques to isolate the \(\sin{x}\), \(\cos{x}\), or \(\tan{x}\) terms. This might include combining like terms, factoring, finding LCD's, etc.
- Determine the specific solutions on \([0, 2\pi)\) for the equations \(\sin{x} = a\), \(\cos{x} = b\), or \(\tan{x} = c\) using the unit circle. If the \(a\), \(b\), and \(c\) values are not nice unit circle values, then we might need to use technology to compute the corresponding inverse trig value.
- Express the infinitely many solutions by adding \(2\pi k\) for sine and cosine or \(\pi k\) for tangent.
Let's look at a few examples.
