How Do You Calculate the Angle and Area in Trigonometry Problems?

  • Thread starter Thread starter rocomath
  • Start date Start date
  • Tags Tags
    Applications Trig
Click For Summary
SUMMARY

This discussion focuses on calculating angles and areas in trigonometry, specifically addressing two problems involving gears and the area of a parallelogram. The first problem requires finding the angle \phi based on the interaction of gears, where the assumption of adding their radii is questioned. The second problem confirms that the area of a parallelogram is indeed the product of two adjacent sides multiplied by the sine of the included angle, aligning with established trigonometric principles.

PREREQUISITES
  • Understanding of trigonometric functions, particularly sine.
  • Familiarity with the properties of parallelograms.
  • Knowledge of angular and linear speed concepts.
  • Basic geometry involving angles and areas.
NEXT STEPS
  • Study the relationship between linear and angular speed in rotating systems.
  • Explore the derivation of the area formula for triangles and parallelograms.
  • Investigate the application of sine in various geometric contexts.
  • Practice solving problems involving gears and their interactions in mechanical systems.
USEFUL FOR

Students studying trigonometry, educators teaching geometry, and anyone involved in mechanical engineering or physics applications related to gears and rotational motion.

rocomath
Messages
1,752
Reaction score
1

Homework Statement


32. Three gears are arranged as shown in the figure below. Find the angle \phi

46. Prove that the area of a parallelogram is the product of two adjacent sides and the sine of the included angle.


Homework Equations





The Attempt at a Solution


32. I assumed that since the gears touch that I could add their radius. Would that be incorrect? I was thinking I had to use the linear and angular speed formulas, but I wasn't sure. I know that their linear speed is equal, but I don't think I need to do all that.
1237066652_ceb0df7e04_o.jpg

46. I followed the steps in which they obtained the Area of a triangle.
1237066166_574df86db0_o.jpg
 
Physics news on Phys.org
Both workings seem find to me.
 

Similar threads

Trigonometry: finding an angle, area and length of sector of a circle
  • · Replies 2 ·
Replies
2
Views
2K
How Can I Calculate the Height of a Building Using Right Angle Trigonometry?
  • · Replies 11 ·
Replies
11
Views
6K
Trigonometry problem involving cylinders.
  • · Replies 3 ·
Replies
3
Views
4K
How Do You Calculate the Distance Between Adjacent Numbers on a Clock Face?
  • · Replies 2 ·
Replies
2
Views
2K
How Do You Calculate the Total Area of Rectangles and Triangles Combined?
  • · Replies 3 ·
Replies
3
Views
2K
Finding the Area of a Parallelogram with Given Sides and Angle
  • · Replies 10 ·
Replies
10
Views
7K
High School How Can Trigonometry Calculate Distances in Surveying?
  • · Replies 5 ·
Replies
5
Views
3K
A very formulaic trig word problem (find an angle)
  • · Replies 9 ·
Replies
9
Views
3K
How Do You Solve Trigonometry Problems Involving Satellites and Angles?
  • · Replies 2 ·
Replies
2
Views
5K
Area of a sector without knowing the angle (can't use a calculator)
  • · Replies 6 ·
Replies
6
Views
11K