Unlocking the Mysteries of Trigonometry
Unlocking the Mysteries of Trigonometry
Learning objective
Items in this lesson
Unlocking the Mysteries of Trigonometry
Learning objective
What do you already know about the relationships between angles and sides in triangles?
What is Trigonometry?
Trigonometry studies relationships between angles and sides of triangles. Essential in fields like physics, engineering, and architecture.
Introduction to Pythagoras' Theorem
A² + B² = C². Used to find the length of a side in a right-angled triangle.
Understanding TOA CAH SOH
A mnemonic for remembering Tangent, Cosine, and Sine ratios: Tan = Opp/Adj, Cos = Adj/Hyp, Sin = Opp/Hyp.
Pythagoras' Theorem Example
Given a right triangle with legs 3 and 4, find the hypotenuse.
TOA CAH SOH Example
Find Sin, Cos, Tan of a 30° angle in a 30-60-90 triangle.
Interactive: Triangle Solver
Use an interactive tool to solve triangle problems by applying learned concepts.
Introduction to Sine Rule
a/sinA = b/sinB = c/sinC, used to find unknown lengths or angles in non-right triangles.
Sine Rule Example - Finding Length
In a triangle with angles 45°, 55°, and 80° and side 7 opposite 45°, find the side opposite 55°.
Sine Rule Example - Finding Angle
Given sides 8, 9 and angle opposite 8 is 60°, find the angle opposite side 9.
Sine Rule for Area of Triangle
Area = 1/2 * a * b * sinC. Use for non-right triangles where two sides and an angle are known.
Sine Rule Area Example
Calculate the area of a triangle with sides 5, 7 and angle 60° between them.
Introduction to Cosine Rule
c² = a² + b² - 2ab * cosC, used for finding a side or angle in any triangle.
Cosine Rule Example - Finding Side
Find side c in a triangle with sides 7, 10 and angle 45° between them.
Cosine Rule Example - Finding Angle
Given sides 8, 6, and 5, find the angle opposite side 5.
Comparing Sine and Cosine Rules
Both rules apply to non-right triangles but are used in different scenarios.
Recap of Key Concepts
Review Pythagoras’ Theorem, TOA CAH SOH, Sine and Cosine rules.
Quiz: Test Your Knowledge
Answer multiple-choice questions on trigonometry concepts covered.
Discussion: Real-World Applications
How is trigonometry used in architecture, engineering, and astronomy?
