# Calculating theta from alpha: Tan(theta)=Cot(alpha)

• Shivam
In summary: Looks right to me, though it seems (4) should also be valid since the question does not indicate whether the angle is to be measured from the half plane below impact or from the half plane above it.
Shivam
Homework Statement
The angle theta with the inclined plane which the velocity makes just after 1st impact will be ?
Relevant Equations
Conservation of linear Momentum. Coefficient of restitution.

After impact VCos(alpha) will be normal to the inclined, now i calculated for theta by using [ Tan(theta) = vCos(alpha)/vSin(alpha),. Tan(theta)= Cot(alpha) ]. I don't know how to solve further to get value of theta, according to book thta = alpha.

Shivam said:
I don't know how to solve further to get value of theta, according to book thta = alpha.

The answer fron the book is incorrect. However, the way figure is drawn may make it appear to be correct. Since the result has to work for an arbitrary angle ##\alpha##, I suggest that you redraw the figure using a value of ##\alpha## that is not so close to 45 deg.

Try answering these questions; they should make the correct solution clear:
- What angle will the velocity make with the plane before impact?
- How will the velocity after impact be related to the velocity before impact?

Shivam
tnich said:
The answer fron the book is incorrect. However, the way figure is drawn may make it appear to be correct. Since the result has to work for an arbitrary angle ##\alpha##, I suggest that you redraw the figure using a value of ##\alpha## that is not so close to 45 deg.

Try answering these questions; they should make the correct solution clear:
- What angle will the velocity make with the plane before impact?
- How will the velocity after impact be related to the velocity before impact?
Bro , i thought geometrically and angle was not equal to alpha , i also tried this [ Tan(theta) = Cot(alpha),
Tan(theta) = Tan(90-alphal),
So, theta = 90 - alpha],
is it correct

tnich
Shivam said:
Bro , i thought geometrically and angle was not equal to alpha , i also tried this [ Tan(theta) = Cot(alpha),
Tan(theta) = Tan(90-alphal),
So, theta = 90 - alpha],
is it correct
Looks right to me, though it seems (4) should also be valid since the question does not indicate whether the angle is to be measured from the half plane below impact or from the half plane above it.

Shivam

## 1. What is the difference between theta and alpha in this equation?

Theta and alpha are both Greek letters used in mathematics to represent angles. In this equation, theta represents the angle in radians, while alpha represents the angle in degrees.

## 2. How do you calculate theta from alpha using this equation?

To calculate theta from alpha using this equation, you first need to convert alpha from degrees to radians by multiplying it by pi/180. Then, use the inverse tangent function (tan^-1) to find theta. The equation should look like this: theta = tan^-1(cot(alpha * pi/180)).

## 3. What is the purpose of calculating theta from alpha?

Calculating theta from alpha is useful in solving trigonometric problems that involve angles in both degrees and radians. It allows you to convert between the two units and find the corresponding angle.

## 4. Can you use this equation to find theta or alpha if you only know one of them?

Yes, you can use this equation to find theta if you know alpha or vice versa. However, it is important to remember to convert the angle to the correct unit (degrees or radians) before plugging it into the equation.

## 5. Are there any limitations to this equation?

Yes, this equation is limited to finding the theta and alpha values for right-angled triangles. It cannot be used for other types of triangles or angles.

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