Positive and Negative Angles

Introduction to Positive and Negative Angles:

An ANGLE is strong-minded by rotating a ray about it's endpoint. The initial location of the ray is the INITIAL SIDE of the angle, and the ending position of the ray is its TERMINAL SIDE. The endpoint of ray called the VERTEX.

The unit circle of the angle is said to be in STANDARD POSITION because its vertex is the origin, and its initial side lies on the x-axis. This is also called positive angle, meaning it's created by a COUNTERCLOCKWISE rotation.
The unit circle of angle is in standard position, but it's called a NEGATIVE ANGLE, since it is created by a CLOCKWISE rotation. I like to share this Inscribed Angles with you all through my article.


Rules of Positive and Negative angles:

Positive Angle:

An angle formed by anti-clockwise rotation is a positive angle. In the figure initial side is OX. When these side is rotated by an angle θ in counter clockwise direction then angle is generated is called positive angle.

Negative Angle:

An angle generated by clockwise rotation is a positive angle. In these diagram let the initial side is OX. When these side is rotated by an angle θ in clockwise direction then angle called as negative angle.

Rule I:

Sign of an angle is always positive when measured in anti-clockwise direction.

Rule II:

Sign of an angle is always negative when measured in clockwise direction. Understanding Volume of Right Prism is always challenging for me but thanks to all math help websites to help me out.


Example of Positive and Negative Angles:

Positive and Negative Angles:

Positive Angles start from 0 degrees and turn around counterclockwise.

Negative Angles start from 0 degrees and turn around clockwise.

You can translate your negative angle to its equivalent positive angle by adding 360 degrees to it until it turns positive.

Once it is positive, you can pleasure it the same as you would any other positive angle in the quadrant that it is in.

Example 1:

Angle is -135 degrees.

sum  360 degrees to it until it turns positive.

It turn positive then first time we add 360 degrees to it.

The equivalent is positive angle is 225 degrees.

It is in the quadrant of 3.

Example 2:

Is 300 not same as -300?

Solution:

The answer to this question is NO. Here why the angle have  two attributes attached to it: Degree of rotation (or magnitude of rotation) and Direction of rotation (clockwise or anticlockwise). While those wo angles have same degree of rotation, direction of rotation is just opposite as signified by there opposite signs. Therefore those two angles are different.

Angle of Rotational Symmetry

Introduction to angle of rotational symmetry:

Rotational symmetry is definite as angle, while we rotate as alternate a shape in its center point; you may notice that at a certain angle, the shape coincides with its not rotated itself. When this happens, the shape is said that it have rotational symmetry. A shape has rotational symmetry if it fits on to itself two or more times in one turn. The number of times the rotational symmetry is the shape fits on to itself in one turn. Is this topic Straight Angle Definition hard for you? Watch out for my coming posts.


Type of symmetry:

Symmetry has,

Line symmetry
2D rotational symmetry
3D rotational symmetry
A 2D shape has a line of symmetry if the lines separate the shape into two share equally – one being the mirror image of the other.

Rotation: whatever rotate the shape on it around, every rotation has depending on center point and an angle.

Translation:  Translation is to be in motion without rotating or reflecting, every translation has depending on distance and

a direction.

Reflection: reflection is seemed mirror image. Every reflection has a mirror line.

Glide Reflection: With the direction of the reflection line, glide reflection is the symmetry of its collection of reflection and  translation.

Angle of rotation:


When you can turn a figure around a center point by less than 270° and the figure appear that there is no changed, and then the figure has rotation symmetry. The middle of rotation, and then the smallest angle require turning and the point around which you rotate is called the angle of rotation.

For instance take any figure on the left can be turned by 160 degree the same way you would turn an hourglass and it look like the same. Her take 2nd figure one can be turned by 120 degree and other one is 72 degree. The 2nd figure comes from 72 degree that it has five points, just rotate it until it looks the same; we need to make 1 / 5 of a completed 360 degree. So 1 / 5 * 360 degree = 72 degree.

Geometry Book Answers

Introduction:

Geometry is nothing but the act of determining the dimensions or volume of an object. Buildings, cars, planes, maps are of great examples of geometry. The plane geometry, normally used in finding the area, perimeter, circumference of  Two-dimensional figures like triangle, circle, rectangle, rhombus, trapezoid, quadrilateral etc.  Let us solve some sample problems from plane geometry. Understanding Geometry Lines is always challenging for me but thanks to all math help websites to help me out.


Sample Geometry Problems:


Example 1:
The radius of a right circular cylinder is 7 cm and its height is 20 cm. Find its curved surface area and total surface area.

Solution:
Radius(r) = 7cm, Height(h) = 20 cm.


Curved surface area = (2`pi`r h )= 2 * 22 / 7 * 7 * 20 cm^2

= 880 cm^2

Area of the base and the top    = (2`pi`r2)

= 2 * (22 / 7) * 7 * 7 cm^2

= 308 cm^2

Total surface area = (2`pi`r h) + (2`pi`r2) = 880 cm^2 + 308 cm^2

= 1188 cm^2

Example 2:

Surface area of a right circular cylinder of height 35 cm is 121 cm^2. find the radius of the base.

Solution:

Curved surface area = (2`pi`r h) = 121 cm^2

2*(22/7)* r *35 = 121

r = (7*121)/(2*22*35)

= 11/20

= 0.55 cm

Hence, radius of the base = 0.55 cm.

Example 3:

Curved surface area of a right circular cylinder is 6.6 m^2. if the radius of the base of the cylinder is 1.4 m , find the height.

Solution:

Curved surface area = (2`pi`r h) = 6.6

= 2 * (22/7) * 1.4 * h

= h = (7*6.6) / (2*22*1.4)

= (7*66) / (2*22*14)

= 3/4 = 0.75

Required height of the cylinder = 0.75 m.

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Geometry Practice Exam Problems:


1. the circumference of the base of a right circular cylinder is 220cm. if the height of the cylinder is 2m, find the lateral surface area of the cylinder.

2. A closed circular cylinder has diameter 20cm and height 30 cm. find the total surface area of the cylinder.

3. the radius of the base of a closed right circular cylider is 35 cm and its height is 0.5m. find the total surface area of the cylinder.

Answers:

1. 4.4 m^2

2. 2512 cm^2

3. 18700 cm^2