Need help determining whether to use cosine or sine

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SUMMARY

This discussion clarifies the application of sine and cosine in physics problems, specifically in the context of forces acting at an angle. The key takeaway is that when analyzing forces, the weight (mg) should be treated as the hypotenuse of a right triangle. The components of the weight are defined as mgcos(beta) for the adjacent side and mgsin(beta) for the opposite side, depending on the angle beta. Understanding this relationship is crucial for solving problems involving inclined planes and other scenarios where angles are involved.

PREREQUISITES
  • Understanding of basic trigonometry, including sine and cosine functions.
  • Familiarity with the concept of forces in physics, particularly weight as a vector.
  • Knowledge of right triangles and how to visualize angles and their components.
  • Ability to interpret physics problems involving angles and forces.
NEXT STEPS
  • Study the application of trigonometric functions in physics problems involving inclined planes.
  • Learn how to construct and analyze right triangles in the context of force decomposition.
  • Explore examples of real-world applications of sine and cosine in physics, such as projectile motion.
  • Investigate the relationship between angles and force components in various physical scenarios.
USEFUL FOR

Students studying physics, educators teaching trigonometry and physics concepts, and anyone looking to deepen their understanding of force analysis in angled situations.

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I'm having trouble understanding when to use sine or cosine in my physics problems

for example I got this from one of the lectures off youtube
and I know why they are using sine and cos because it is at an angle but I'm rotating the angle to understand why it is mgcosbeta and why the other is mgsinbeta and not the other way around

could someone explain to me why it is mgcosbetahttp://img213.imageshack.us/img213/8798/91559741.png
 
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physicsnoob145 said:
I'm having trouble understanding when to use sine or cosine in my physics problems

for example I got this from one of the lectures off youtube
and I know why they are using sine and cos because it is at an angle but I'm rotating the angle to understand why it is mgcosbeta and why the other is mgsinbeta and not the other way around

could someone explain to me why it is mgcosbeta
Visualize what it looks like when the angle is set to 0. One will be 0 and the other will be mg. The one that is 0 is sin and the one that is mg is cos. That will always work.
 
Last edited:
It helps to understand this if you construct a triangle with mg as the hypotenuse, then it becomes clear when to use sin or cosine.
 

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rcgldr said:
It helps to understand this if you construct a triangle with mg as the hypotenuse, then it becomes clear when to use sin or cosine.

thank you it is a little clearer now
 
Just as rcgldr has shown the weight must always be the hypotenuse as it is largest force acting.
 

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