#26 Trigonometry - Edexcel IGCSE Exam Questions

Summary

In this video, Mr. Aspey walks through several trigonometry problems typically found in the IGCSE exam. He explains step-by-step how to identify the sides of a triangle (opposite, adjacent, hypotenuse) and choose the appropriate trigonometric function (cosine, sine, or tangent) to solve for unknown sides or angles. Throughout the video, Mr. Aspey demonstrates the use of a calculator to perform trigonometric calculations and emphasizes the importance of understanding triangle properties to tackle complex questions. The video concludes with a detailed solution to a perimeter problem involving multiple triangles.

Takeaways

• 📐 Label the sides of the triangle correctly by identifying the opposite, adjacent, and hypotenuse based on the angle and right angle.
• 🧮 To find PQ, use the cosine rule: cos(angle) = adjacent/hypotenuse, then calculate hypotenuse using the formula H = A/cos(angle).
• 📊 For the second triangle, to find EG, use cosine again: cos(angle) = adjacent/hypotenuse. Apply the formula to calculate the side length.
• ✖️ To solve the second triangle, use the known side length and angle to calculate the adjacent side using tan: tan(angle) = opposite/adjacent.
• 📏 For more complex triangles, break down the larger shape into smaller triangles to solve unknown sides or angles using trigonometric identities.
• 🔺 Use the inverse of tan (tan-1) when solving for an unknown angle with known opposite and adjacent sides.
• 📉 Work out multiple steps by finding intermediate side lengths and angles in small triangles before solving the larger figure.
• 🧩 Drawing extra lines (like perpendiculars) can help simplify complex trapezium problems by creating right-angle triangles.
• 📏 Use trigonometric functions like sine, cosine, and tangent to solve for missing sides and angles when working with trapeziums.
• 📝 For perimeter questions involving repeated shapes, calculate individual side lengths and sum them up, accounting for repeated sides.

Q & A

What is the first step in solving a trigonometry problem involving right-angled triangles?

The first step is to label the sides of the triangle. You need to identify the 'opposite', 'adjacent', and 'hypotenuse' sides relative to the given angle.

Which trigonometric ratio is used when you know the adjacent and need to find the hypotenuse?

The cosine ratio is used when you know the adjacent side and need to find the hypotenuse. The formula is cos(angle) = adjacent/hypotenuse.

How do you solve for the hypotenuse if you know the adjacent side and the angle?

To solve for the hypotenuse (H), use the formula H = adjacent / cos(angle). Substitute the known values into this equation.

In the script, how is PQ calculated?

PQ is calculated by using the cosine rule: PQ = 24.3 / cos(63). When entered into a calculator, it results in 53.5.

What trigonometric ratio is used when finding a side opposite to a known angle?

The sine ratio is used when finding a side opposite a known angle. The formula is sin(angle) = opposite/hypotenuse.

How is the adjacent side (A) found when the opposite and angle are known?

To find the adjacent side (A) when the opposite is known, use the tangent formula: A = opposite / tan(angle).

How is the angle in a triangle calculated if you know the opposite and adjacent sides?

The angle is calculated using the inverse tangent function (tan^-1). The formula is angle = tan^-1(opposite/adjacent).

In the perimeter problem of the trapezium, what was the process for finding the total perimeter?

The total perimeter was calculated by finding each side of the trapezium using trigonometry (adjacent and hypotenuse) and adding them together. The final perimeter was 101.4 cm.

How is the hypotenuse calculated in the problem involving the shape with five triangles?

The hypotenuse was calculated using Pythagoras' theorem: hypotenuse^2 = opposite^2 + adjacent^2. The final hypotenuse was 13.5 units.

What formula is used to calculate the total perimeter of the shape with five triangles?

To calculate the total perimeter, the lengths of the five hypotenuses and five short sides were added together. The total perimeter was calculated as 111 units.