This page gives you the key ideas to recognise before you start a question. The full course then takes you through the method, exam-style practice and fully worked solutions.
Know exact values
Be fluent with the standard sine, cosine and tangent values. Exact forms are often required rather than decimals.
Read the interval
When solving a trigonometric equation, the stated interval controls how many solutions you must find.
Use identities strategically
Identities can turn an unfamiliar expression into a solvable equation. Look for a common function or a form you can factorise.
Link equations and graphs
The periodic shape of sine, cosine and tangent explains repeated solutions and helps you check whether answers are plausible.
Worked example: solve on an interval
Solve sin x = 1/2 for 0° ≤ x ≤ 360°:
Reference angle = 30°
Sine is positive in quadrants I and II
x = 30°, 150°
Reference angle = 30°
Sine is positive in quadrants I and II
x = 30°, 150°
Common mistakes to avoid
- Stopping after the calculator gives the first solution.
- Mixing degrees and radians.
- Rounding an answer when an exact value is required.