Right Triangle Trigonometry Lecture Notes

Introduction to Right Triangle Trigonometry

• SOA Expression: Introduction to the term, but the focus is on right triangle trigonometry.
• Triangle Sides:
  • Opposite side (relative to angle Theta)
  • Adjacent side (next to angle Theta)
  • Hypotenuse (the longest side, opposite the right angle)

Pythagorean Theorem

• Formula: (a^2 + b^2 = c^2)
• Not the main focus but essential for finding missing sides of right triangles.

Six Trigonometric Functions

• Sine (sin Θ): Opposite / Hypotenuse
• Cosine (cos Θ): Adjacent / Hypotenuse
• Tangent (tan Θ): Opposite / Adjacent
• Cosecant (csc Θ): Reciprocal of sine (Hypotenuse / Opposite)
• Secant (sec Θ): Reciprocal of cosine (Hypotenuse / Adjacent)
• Cotangent (cot Θ): Reciprocal of tangent (Adjacent / Opposite)

Example Problems

Problem 1: Right Triangle with Sides 3, 4, and Hypotenuse 5

• Use Pythagorean theorem to find the hypotenuse: 3^2 + 4^2 = 5^2.
• Trig function values:
  • sin Θ = 4/5
  • cos Θ = 3/5
  • tan Θ = 4/3
  • Reciprocal functions: csc, sec, and cot by flipping the above fractions.

Problem 2: Right Triangle with Sides 8, Hypotenuse 17

• Recognize special triangles like 8-15-17.
• Trig function values:
  • sin Θ = 15/17
  • cos Θ = 8/17
  • tan Θ = 15/8
  • Reciprocal functions using the reciprocals of the above.

Problem 3: Right Triangle with Hypotenuse 25, Side 15

• Recognize 3-4-5 family multiplied by 5.
• Trig function values:
  • sin Θ = 4/5
  • cos Θ = 3/5
  • tan Θ = 4/3

Finding Angles with Trigonometric Functions

• Angle Calculation Example:
  • Use tangent function to find angles when given opposite and adjacent sides.
  • Example: Calculate angle using tan Θ = 5/4.

Trigonometry Course Information

• Available on Udemy, topics include unit circle, solving triangles, graphing trig functions, and more.
• Ongoing additions to the course, such as laws of sines and cosines, polar coordinates.

Additional Concepts

• Special Right Triangles: 3-4-5, 5-12-13, 8-15-17, other multiples.
• Verifying Trig Identities: Highlighted as a challenging section.
• Advanced Topics: Sum and difference formulas, double and half-angle formulas, solving trig equations.

These notes cover the key points from the lecture on right triangle trigonometry, including definitions, example problems, and trigonometric functions. They also provide a brief overview of an online trigonometry course available for further learning.