# Equivalent angles and Trig Fucntions

• TheCammen
In summary, the conversation discusses the forces acting on a block held on an overhang and the steps to determine the normal and frictional forces, as well as the angles at which the block will remain at rest. The solution involves splitting the weight of the block into perpendicular and parallel components, and using trigonometric functions to determine the forces and angles.
TheCammen

## Homework Statement

A block with mass M is held statically on an overhang by a force Mg applied horizontally and the force of friction on the overhang. What are the normal and frictional forces? For what angles θ does the block remain at rest?

## The Attempt at a Solution

In the picture I've drawn out the forces acting on the block. I understand the ideas behind static equilibrium. What I have trouble with is understanding which trig functions to use when comparing the forces and how to identify which angles are equivalent to the angle θ in the problem. Can anyone explain the thought process behind determining these things?

#### Attachments

• Block Overhang.jpg
13.6 KB · Views: 494
To get the forces N and Ff, you will have to split the weight into two components, one perpendicular to the plane and one parallel to the plane. If we redraw the two forces like this: (reducing the block to a small point)

The angle formed by the line mg and the horizontal is 90 degrees and the angle formed by the normal of the plane and the plane itself is?

When you get that you can easily see where the angle a will be in relation to N and mg.

Draw in the 90 degree angles one at a time for each triangle.

The force that keep the block from falling is a component of frictional force.
FfSinθ=mg

## 1. What are equivalent angles?

Equivalent angles are angles that have the same measure. This means that they have the same degree of rotation and thus create the same shape when drawn.

## 2. How can I find equivalent angles in a triangle?

In a triangle, the sum of the interior angles is always 180 degrees. This means that if you know the measures of two angles, you can find the measure of the third angle by subtracting the sum from 180 degrees.

## 3. What are the six trigonometric functions?

The six trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are used to relate the side lengths of a right triangle to its angles.

## 4. How can I use trigonometric functions to solve for missing angles or side lengths?

By knowing the values of two sides and one angle, you can use the trigonometric functions to solve for the missing side or angle. For example, if you know the length of the hypotenuse and one of the acute angles in a right triangle, you can use the sine function to find the length of the opposite side.

## 5. What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1 unit and its center at the origin (0,0) on the coordinate plane. The unit circle is used in trigonometry to visualize the relationships between the trigonometric functions and the angles in a right triangle. It is also used to extend the definitions of these functions to angles greater than 90 degrees or less than 0 degrees.

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