Trigonometry
What you must understand
Trigonometry connects angles and side lengths in triangles. In a right triangle, use SOH–CAH–TOA: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Know the Pythagorean theorem and the fact that the angles in a triangle sum to 180°. Be able to solve for a missing side or angle, and set up problems involving angles of elevation and depression.
For the sine and cosine laws, use the sine law a/sin A = b/sin B = c/sin C when you know a matching side–angle pair, and the cosine law c² = a² + b² − 2ab·cos C when you know two sides and the included angle (or all three sides). Understand the ambiguous case of the sine law, where two triangles can satisfy the given data. Know the unit circle, radian measure, and how to convert between degrees and radians (180° = π radians).
Traps to watch for
- Using the wrong ratio (mixing up opposite and adjacent).
- Forgetting to set the calculator to the correct degree or radian mode.
- Applying the sine law without a matching side–angle pair.
- Ignoring the ambiguous case when an angle is not included.
- Confusing angle of elevation (looking up) with depression (looking down).
Rule of thumb
Match what you know to the formula: sine law needs a side–angle pair; cosine law needs two sides with the included angle or all three sides.
Worked example: Convert 150° to radians: 150 × π/180 = 5π/6.