Ginger Math Petition Video: Trigonometry Crash Course

Introduction

• Focus on trigonometry skills: Sine rule, Cosine rule, and SOHCAHTOA.
• Derived from audience demand via a poll.
• Accompanied by a formula list for Sine rule, Cosine rule, and area of a triangle.

Key Topics Covered

Question Walkthrough

1. Question 7: Calculating AD

   • Scenario: AB is a vertical tower (30m), angle ABC is 68°, BD is 36m.
   • Approach: Recognize a right-angled triangle; use Pythagoras instead of trigonometry.
   • Solution: Use Pythagorean theorem to calculate AD:
     • Formula: ( x = \sqrt{36^2 - 30^2} )
     • Result: AD = 19.9m (to three significant figures).

2. Calculating AC

   • Approach: Use trigonometry with SOHCAHTOA.
   • Solution:
     • Identify sides: Opposite = 30m, Angle = 68°, Adjacent = AC.
     • Use tangent: ( AC = \frac{30}{\tan(68°)} )
     • Result: AC = 12.1m (to three significant figures).

3. Question 11: Use of Cosine Rule

   • Objective: Show that a given quadratic is true.
   • Cosine Rule Formula: ( c^2 = a^2 + b^2 - 2ab \cos C )
   • Procedure: Substitute values and simplify to a quadratic form.
   • Calculation Result: Confirmed quadratic equation.

4. Calculating Angle DBC

   • Approach: Use angles on a straight line and the Sine Rule.
   • Solution: Calculate using inverse sine and adjust for rounding errors.
   • Result: Angle DBC = 20.4°

5. Area of Triangle ABC

   • Formula: ( \text{Area} = \frac{1}{2}ab \sin C )
   • Calculation: Use obtained angles and sides.
   • Result: Area = 48.1 square meters.

Additional Questions

6. Question 5: Trigonometry in Different Triangle Scenarios

   • Objective: Confirm side lengths using given areas and angles.
   • Solution: Apply area formula and cosine rule for confirmation.

7. Question 9: Applying Cosine Rule for Angle Calculation

   • Process: Learn the rearranged formula for angle calculation.
   • Implementation: Substitute and solve using cosine function.
   • Result: Correct angle calculation.

8. Question 3: Easier Trigonometry Applications

   • Tasks: Calculate sides using SOHCAHTOA and verify using tan.
   • Results: Confirm lengths and verify using calculator results.

Tips and Tricks

• Always check mode on calculator (DEG or RAD).
• Use exact values to minimize rounding errors.
• Store values on calculators to avoid errors in complex calculations.
• Understand the layout of formula sheets and know exact trigonometric values.
• Thoroughly practice different styles of questions to enhance understanding.

Conclusion

• Emphasize practice through additional resources provided.
• Encourage understanding of trigonometry through varied question practices.
• Importance of formula memorization and calculator proficiency.

Additional Resources

• PowerPoint with extra practice questions available in the video description for further study.