1. Fundamentals of Mathematics for Engineers Lab ENGR 2194 Lab # 2 – Trigonometric Relationships: One and Two-Link Planar Robots

2. Real-World Example Related to Topic! Automotive, aerospace, robotics and building design engineers commonly use: Trigonometry Geometrical relationships Inventor Dean Kamen with Prosthetic Arm

3. Today's Learning Objectives  After today's lab, students will be able to: 1.Understand the basic trigonometric functions. 2.Understand the concept of a unit circle and four quadrants. 3.Understand the concept of a reference angle. 4.Be able to perform the polar to rectangular and rectangular to polar coordinate conversion. 5.Prove a few of the basic trigonometric identities.

4. Reference Angle  Commonly represented as Greek letter ϕ  Less than 90 °

5. Law of Cosines

6. Law of Sines

7. MATLAB  Commands (e.g., “disp”)  Functions (e.g., sin/sind, cos/cosd, etc.)  Dot Operators

8. Lab Equipment Angle 1 = 30 degrees Angle 2 = 30 degrees

9. Lab Equipment Angle 1 = 30 degrees Angle 2 = 45 degrees

10. Lab Equipment Angle 1 = 30 degrees Angle 2 = 60 degrees

11. Important Takeaways  Essential to Engineers: Trigonometry  Basic functions  Unit circle and four quadrants  Reference angle  Coordinate conversions  Basic identities Technical Computing  MATLAB

12. Preview of Next Lab  MATLAB Supplemental Instruction #1 Plotting  Multiple graphs  Line identifiers  Legend