Arithmetic Symbols
Addition (+)
• The plus symbol (+) is used to represent addition, which is the process of combining two or more numbers to find their total sum.
Subtraction (-)
• The minus symbol (-) is used to represent subtraction, which is the process of taking one number away from another to find the difference.
Multiplication (× or *)
• The multiplication symbol (× or *) is used to represent multiplication, which is the process of repeated addition. It is used to find the total when a number is multiplied by another number.
Division (÷ or /)
• The division symbol (÷ or /) is used to represent division, which is the process of dividing one number by another to find the quotient or the number of times one number is contained in another.
Algebraic Symbols
Variables
• Variables are symbols used to represent unknown quantities or values in mathematical equations. Examples include x, y, and z.
Constants
• Constants are fixed values that do not change. Examples include numbers like 3, 5, and 10.
Mathematical Operations
• Mathematical operations are symbols used to perform calculations. Examples include + (addition), - (subtraction), * (multiplication), and / (division).
Geometric Symbols
Shapes
•
Circle: A
closed curve with all points equidistant from the center.
•
Triangle: A
polygon with three sides
and three angles.
•
Square: A polygon with four equal sides and four right angles.
•
Rectangle: A
polygon with four right angles and
opposite sides of equal length.
•
Pentagon: A
polygon with five sides and five angles.
•
Hexagon: A
polygon with six sides and six angles.
• Octagon: A polygon with eight sides and eight angles.
Angles
• Right Angle: An angle that measures 90 degrees.
•
Acute Angle: An angle that measures less than 90 degrees.
•
Obtuse Angle: An angle that measures more than 90
degrees but less than 180 degrees.
•
Straight Angle: An angle that measures 180 degrees.
• Reflex Angle: An angle that measures more than 180 degrees but less than 360 degrees.
Measurements
•
Diameter:
The distance across a circle through its center.
•
Radius: The distance from the
center of
a circle to any point on the
circle.
•
Perimeter: The distance around the outside of a shape.
•
Area: The amount of space inside a shape.
•
Volume: The amount of space occupied by a three-dimensional shape.
• Surface Area: The total area of all the faces of a three-dimensional shape.
Trigonometric Symbols
Sine (sin)
The sine function relates the ratio of the length of the side opposite an angle
to the length of the hypotenuse in a right triangle.
Cosine (cos)
The cosine function relates the ratio of the length of the side
adjacent to an angle to the length of the hypotenuse in a right triangle.
Tangent (tan)
The tangent function relates the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle in a right triangle.
Inverse Sine (arcsin or sin^-1)
The inverse sine function returns the angle whose sine is a given number.
Inverse Cosine (arccos or cos^-1)
The inverse cosine function returns the angle
whose cosine is a given number.
Inverse Tangent (arctan or tan^-1)
The inverse tangent function returns the angle whose tangent is a given number.
Trigonometry Basics
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems in various fields, including engineering, physics, and astronomy.
Trigonometric Functions
The three basic trigonometric functions are sine, cosine, and tangent. These functions are defined as ratios of the sides of a right triangle, and they are used to solve problems involving angles and distances.
Applications of Trigonometry
Trigonometry
has
many practical applications in various fields, including:
•
Engineering: Trigonometry is used to design and analyze structures, such as bridges
and buildings.
•
Physics: Trigonometry
is
used
to
model the motion of objects, such as projectiles and pendulums.
• Astronomy: Trigonometry is used to calculate the positions of stars and planets in the sky.
Calculus Symbols
Derivatives
•
The
derivative of a function represents its rate of change
at any given point. It is denoted using the symbol 'd' or 'dx'.
• Example: d/dx represents the derivative with respect to x.
Integrals
•
The integral of a function represents the
accumulation of its values over a given interval. It is denoted using the symbol '∫'.
• Example: ∫f(x)dx represents the integral of f(x) with respect to x.
Limits
•
The
limit of a function represents its behavior as the input approaches a certain value. It is denoted using the symbol 'lim'.
• Example: lim(x→a) represents the limit of x as it approaches a.