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Understanding Right Triangle Trigonometry

Apr 25, 2025

Lecture Notes: Right Triangle Trigonometry

Introduction to Right Triangle Trigonometry

  • SOA Expression: Introduction to the concept
  • Angle Theta (θ):
    • Opposite Side: Side opposite to the angle
    • Adjacent Side: Side next to the angle
    • Hypotenuse: Longest side, opposite the right angle

Pythagorean Theorem

  • Formula: (a^2 + b^2 = c^2)
  • Not the focus but important to know

Six Trigonometric Functions Using SOA

  1. Sine (sin θ)
    • Formula: (\text{Opposite} / \text{Hypotenuse})
  2. Cosine (cos θ)
    • Formula: (\text{Adjacent} / \text{Hypotenuse})
  3. Tangent (tan θ)
    • Formula: (\text{Opposite} / \text{Adjacent})
  4. Cosecant (csc θ)
    • Reciprocal of sine: (\text{Hypotenuse} / \text{Opposite})
  5. Secant (sec θ)
    • Reciprocal of cosine: (\text{Hypotenuse} / \text{Adjacent})
  6. Cotangent (cot θ)
    • Reciprocal of tangent: (\text{Adjacent} / \text{Opposite})

Solving Right Triangles

  • Example Problems
    • Using known sides to find missing sides with Pythagorean theorem
    • Special right triangles: 3-4-5, 5-12-13, 8-15-17, 7-24-25

Calculating Trigonometric Functions

  • Example: Given triangle sides, calculate sin θ, cos θ, tan θ, csc θ, sec θ, cot θ
  • Special Triangles
    • Multiples of basic special triangles

Using Trigonometry to Find Missing Sides

  • Example: Given side lengths and angles, use trigonometric functions to find missing sides
  • Function Selection: Based on known sides relative to the angle

Using Inverse Functions to Find Angles

  • Finding Angles: Using inverse trigonometric functions (arc functions)
  • Example: Given sides, calculate angles using inverse functions

Course Information

  • Trigonometry Course on Udemy
    • Covers angles, unit circle, right triangle trigonometry
    • Includes solving problems, graphing functions, verifying identities
    • Still in development with more sections to be added

Conclusion

  • Understanding the relationships between sides and angles in right triangles
  • Use of trigonometric identities and special triangles to solve problems effectively

These notes provide a high-level overview of the key concepts discussed during the lecture presentation on right triangle trigonometry.

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