#26 Trigonometry - Edexcel IGCSE Exam Questions

Mr Astbury
7 Apr 202314:14

Summary

TLDRIn 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.

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Related Tags
TrigonometryIGCSE MathsExam PrepCosine RuleTangent RuleMath TutorialGeometryStudy TipsProblem SolvingPythagoras