Geometry and Measures

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Trigonometry: Sine, Cosine, Tangent

Geometry and Measures Trigonometry: Sine, Cosine, Tangent

🎬 Video Tutorial

  • Basic Trigonometry: Sine, cosine, and tangent depend only on angle θ in the right-angled triangle; they do not change with the size of the triangle.
  • Trigonometric Ratios: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
  • Solving for Sides: Use trigonometric ratios with a known angle and side to find missing triangle sides.
  • Finding Angles: Find unknown angles θ using inverse functions like cos⁻¹ on a calculator.
  • Key Angle Values: Memorise trigonometric values for common angles (30°, 45°, 60°) to simplify calculations.

📂 Revision Cards

Definitions, ratios, and visuals of sine, cosine, and tangent shown in a right triangle.
A right triangle with 30° angle, opposite side 4 cm. Using the ratio of sin 30°, solve the hypotenuse, which is 8 cm.
The application of using tangent to find the missing side of a right triangle with a 50-degree angle and a known side of 5 cm.
Finding the angle using cosine in a right triangle with sides 4 cm and 8 cm, showing the calculation cos ? = 1/2 and ? = cos?¹(1/2) = 60°.
Common values of sine, cosine, and tangent for 30°, 60°, and 45° with right triangles and ratios.

💬 ChatCat (AI Math Tutor)

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