Trigonometry Paper 4

SOH CAH TOA

SOH CAH TOA is a mnemonic to remember the three basic trigonometric ratios, which only work in right-angled triangles:

• Opposite is the side opposite the given angle.

• Adjacent is the side next to the given angle.

• Hypotenuse is the longest side (always opposite the right angle).

Trigonometry in Paper 4 requires a strong understanding of concepts, formulas, and problem-solving techniques. Make sure you master the following before attempting Past Paper

These ratios help in finding missing sides or angles in right-angled triangles.

Sine Rule

Phytagoras's Theorem applies only to right-angled triangles and states that:

• c = Hypotenuse (the longest side, opposite the right angle)

• a, b = The other two sides of the triangle

Phytagoras

When to use:
✔ To find a missing side when you know one side and two angles
✔ To find a missing angle when you know two sides and one opposite angle

Cosine Rule

When to use:
✔ To find a missing side when you know two sides and the included angle
✔ To find a missing angle when you know all three sides

Area of Triangle

The formula can be used when two sides and the included angle are known

1️⃣ Draw a perpendicular line from the point to the given line.
2️⃣ Form a right-angled triangle.
3️⃣ Use SOH CAH TOA to calculate the perpendicular distance.
4️⃣ Solve for the distance, which is the shortest length from the point to the line.

Shortest Distance

Finding the Bearing of A from B

🧭 Steps:
1️⃣ Draw a North Line at point B.
2️⃣ Measure the angle clockwise from the North line to line AB.

📌 Important Notes:
✔ The bearings of A from B and B from A always differ by 180°.
✔ A true bearing is always written as three digits (e.g., 072° instead of 72°).

Bearings

PAST PAPER EXAMPLE

Example 1

PAST PAPER QUESTIONS

📌 Explanation by Vanessa Keelia

For Question 9️⃣, 1️⃣5️⃣, and 2️⃣2️⃣.

By completing all the questions in the worksheet, you'll be well-prepared to tackle any trigonometry problems with confidence