Understanding the Trigonometry of an Inclined Plane

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SUMMARY

The discussion centers on the mathematical concepts related to the trigonometry of inclined planes, specifically the behavior of the tangent function in various quadrants. Participants clarify that when tan(theta) is less than one, theta lies between -π/2 and π/4. The confusion arises regarding the signs of sine and cosine in different quadrants, particularly when tan(theta) is greater than or equal to one. The correct interpretation of these trigonometric functions is essential for understanding the geometry of inclined planes.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine, cosine, and tangent.
  • Familiarity with the unit circle and the properties of angles in different quadrants.
  • Basic knowledge of inequalities and their implications in trigonometric contexts.
  • Ability to solve equations involving trigonometric identities.
NEXT STEPS
  • Study the properties of the tangent function and its behavior in different quadrants.
  • Learn about the unit circle and how it relates to trigonometric functions.
  • Explore the implications of trigonometric inequalities in real-world applications.
  • Review the derivation and application of trigonometric identities in solving equations.
USEFUL FOR

Students of mathematics, particularly those studying trigonometry and physics, as well as educators seeking to clarify concepts related to inclined planes and trigonometric functions.

bdolle
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<Moderator's note: Moved from a technical forum and therefore no template.>

I don't understand the math here which is troubling considering I got A's in calc 2 and 3...

I tried to divide both sides by cos(theta) and solve for tantheta. but that gives something different.

Also, what does tantheta>=1 even mean? Is this second quadrant or fourth quadrant?

Thanks!
 

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Nevermind. Got the equation for the tan>1 case (I was thinking tan>0 or tan<0 not 1).

But for the case where tan of theta is less than one, that would mean between pi/4 and pi/2. I'm wondering why sintheta becomes negative and costheta becomes positive.

Any takers?
 
bdolle said:
where tan of theta is less than one, that would mean between pi/4 and pi/2.
Between -π/2 and π/4.
 

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