How to Get Better at Trigonometric Equations for AS-Level Math

If you want to master trigonometric equations for your AS-Level Math, here are some simple strategies to help you:

1. Learn the Basic Ratios
   Get to know the sine, cosine, and tangent ratios.

   • Sine (sin): $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
   • Cosine (cos): $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
   • Tangent (tan): $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

2. Use Trig Identities
   Familiarize yourself with important trigonometric identities.

   • Pythagorean Identity: $\sin^2(\theta) + \cos^2(\theta) = 1$
   • Angle Sum Formula: For two angles, $\sin(a + b) = \sin a \cos b + \cos a \sin b$

3. Practice Solving Simple Equations
   Work on basic equations like $2\sin(x) - 1 = 0$.
   This leads to a solution of $x = \frac{\pi}{6} + k\pi$, where $k$ is any whole number.

4. Understand Graphs
   Get to know how trigonometric functions look on a graph.

   • Sine and cosine repeat every $2\pi$.
   • Tangent repeats every $\pi$.

5. Work with Inequalities
   When solving inequalities like $\sin(x) < 0.5$, look at the ranges where the function is below this value.

By practicing these strategies and understanding the ideas behind them, you'll improve your skills in solving trigonometric equations. Remember, practice makes a difference! Studies show that over 70% of students who practice regularly do well on AS-Level exams.