Summary of "Trigonometry (SOHCAHTOA) - GCSE Maths"

Summary of Key Concepts from "Trigonometry (SOHCAHTOA) - GCSE Maths"

The video covers the fundamentals of using Trigonometry to solve problems involving right-angle triangles, focusing on the SOHCAHTOA mnemonic to remember the Sine, Cosine, and Tangent ratios.

Main Ideas:

Labeling Right-Angle Triangles:
- Hypotenuse: The longest side, opposite the right angle.
- Opposite: The side opposite the angle of interest (often labeled as Theta).
- Adjacent: The side next to the angle of interest.
- The sides can be abbreviated as:
  - Hypotenuse (H)
  - Opposite (O)
  - Adjacent (A)
Trigonometric Ratios:
- Sine (sin): \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \) (SOH)
- Cosine (cos): \( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \) (CAH)
- Tangent (tan): \( \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \) (TOA)
Using Trigonometric Ratios:
- To find a missing side or angle, identify which sides are known and apply the appropriate ratio based on the angle given.

Methodology for Solving Problems:

Identify and Label the Triangle:
- Determine the hypotenuse, opposite, and adjacent sides based on the given angle.
Select the Appropriate Trigonometric Ratio:
- Use SOHCAHTOA to decide whether to use Sine, Cosine, or Tangent based on the sides you have.
Set Up the Equation:
- Substitute known values into the chosen trigonometric equation.
Solve for the Unknown:
- Rearrange and solve the equation, using a calculator as needed.
- Round the answer appropriately (typically to three significant figures).
Inverse Functions for Angles:
- When finding an angle, use the Inverse Functions (sin⁻¹, cos⁻¹, tan⁻¹) to isolate the angle.
Complex Problems:
- For problems involving multiple triangles or additional shapes (like trapeziums), use previously calculated values to aid in finding unknowns.

Example Problems:

Finding a Side:
- Given an angle and one side, use the corresponding ratio to find the missing side.
Finding an Angle:
- Given two sides, use the inverse trigonometric functions to find the angle.
Trapezium Area:
- Use the area formula for a trapezium and find necessary heights using right triangle Trigonometry.