Understanding the Trigonometry of an Inclined Plane

In summary, the conversation discusses the math behind solving for tan theta in different quadrants and the confusion around the values of sine and cosine in the second and fourth quadrants. The original poster mentions getting good grades in calculus, but still struggling with this concept. Eventually, they figure out the equation for when tan theta is greater than one, but still have questions about the scenario when tan theta is less than one.
  • #1
bdolle
10
1
<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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  • #2
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?
 
  • #3
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.
 

Related to Understanding the Trigonometry of an Inclined Plane

1. What is a block on an inclined plane?

A block on an inclined plane refers to a physical scenario where a rectangular block is placed on a tilted surface, also known as an inclined plane. This setup is commonly used in physics experiments to study the relationship between the angle of the inclined plane and the force required to keep the block in place.

2. What factors affect the motion of a block on an inclined plane?

The motion of a block on an inclined plane is affected by several factors, including the angle of the incline, the mass of the block, and the force applied to the block. Additionally, the presence of friction between the block and the inclined plane can also impact its motion.

3. How does the angle of the inclined plane affect the force required to keep the block in place?

As the angle of the inclined plane increases, the force required to keep the block in place also increases. This is because the steeper the incline, the greater the component of the force acting against the block's weight. This relationship can be mathematically described by the formula F = mg sinθ, where F is the force, m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the inclined plane.

4. What is the relationship between the angle of the inclined plane and the acceleration of the block?

The acceleration of the block on an inclined plane is directly proportional to the angle of the incline. This means that as the angle increases, so does the acceleration of the block. The mathematical relationship between the two can be described by the formula a = g sinθ, where a is the acceleration, g is the acceleration due to gravity, and θ is the angle of the inclined plane.

5. How does friction impact the motion of a block on an inclined plane?

Friction between the block and the inclined plane can hinder the motion of the block. This is because friction acts in the opposite direction of the motion, reducing the net force on the block. In some cases, the coefficient of friction can be used to calculate the force of friction and determine its impact on the block's motion.

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