Lecture Notes: Right Triangle Trigonometry

Introduction to Right Triangle Trigonometry

• Focus on right triangle trigonometry.
• Important components of a right triangle:
  • Opposite Side: Opposite to the angle θ.
  • Adjacent Side: Next to the angle θ.
  • Hypotenuse: The longest side, opposite the right angle.
• Pythagorean Theorem: ( a^2 + b^2 = c^2 ).

Six Trigonometric Functions

• SOHCAHTOA as a mnemonic for trigonometric ratios:
  • Sine (sin θ): Opposite/Hypotenuse.
  • Cosine (cos θ): Adjacent/Hypotenuse.
  • Tangent (tan θ): Opposite/Adjacent.
• Reciprocal Trigonometric Functions:
  • Cosecant (csc θ): Hypotenuse/Opposite.
  • Secant (sec θ): Hypotenuse/Adjacent.
  • Cotangent (cot θ): Adjacent/Opposite.

Example Problems and Special Right Triangles

• Finding a missing side using the Pythagorean Theorem:
  • Example with sides 3, 4, and hypotenuse 5.
• Special Right Triangles:
  • 3-4-5, 5-12-13, 8-15-17, 7-24-25.
  • Multiples of these triangles also work (e.g., 6-8-10).

Calculating Trigonometric Functions

• Example 1: Calculate sin θ, cos θ, tan θ for a triangle with sides 3, 4, and hypotenuse 5.
• Example 2: Use a given right triangle (sides 8 and 17) to find the missing side and calculate trigonometric functions.

Using Trigonometric Functions for Angle Calculations

• Example with Given Angles:
  • Use trigonometric functions to find missing sides.
  • Examples include using sin, cos, and tan to solve for sides when an angle is given.
• Inverse Trigonometric Functions:
  • Example: Find angle θ given sides, using functions like arctan, arccos.

Access to Trigonometry Course

• Course Availability:
  • Available on Udemy under "Trigonometry: The Unit Circle, Angles, and Right Triangles".
• Course Content:
  • Covers angles, radians, unit circle, special triangles, graphing trig functions, inverse trig functions.
  • Includes solving trigonometric identities, equations, and applications of trigonometric functions.
  • Course is expanding with additional topics like law of sines, law of cosines, polar coordinates.

Additional Information:

• The lecture provides a comprehensive overview of solving right triangle problems using trigonometry.
• Practical examples help in understanding the application of trigonometric functions and identities.