Trigonometry is a branch of mathematics that deals with the study of angles and the relationships between the sides and angles of triangles. Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. The three main trigonometric functions are sine, cosine, and tangent.

The sine function of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. It is denoted by the abbreviation "sin". The sine function is periodic, with a period of 2π, and its range is between -1 and 1.

sin(θ) = Opposite / Hypotenuse

The cosine function of an angle in a right-angled triangle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It is denoted by the abbreviation "cos". Like the sine function, the cosine function is also periodic, with a period of 2π, and its range is between -1 and 1.

cos(θ) = Adjacent / Hypotenuse

The tangent function of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. It is denoted by the abbreviation "tan". The tangent function is not periodic, and its range is all real numbers.

tan(θ) = Opposite / Adjacent

In addition to sine, cosine, and tangent, there are three reciprocal trigonometric functions: cosecant, secant, and cotangent. These functions are the reciprocals of sine, cosine, and tangent, respectively. They are denoted as csc, sec, and cot.

Trigonometric functions have wide applications in various fields such as physics, engineering, architecture, and more. They are used to model periodic phenomena, analyze waveforms, solve navigation problems, and much more.

To master trigonometric functions, it's essential to understand the definitions of sine, cosine, and tangent, as well as their relationships with the sides of a right-angled triangle. Practice solving trigonometric equations, understanding the unit circle, and applying trigonometric functions to real-world problems. Additionally, familiarize yourself with the graphs of trigonometric functions and their properties.

Remember to also study the reciprocal trigonometric functions and their properties. Practice using trigonometric identities to simplify and solve trigonometric expressions. Finally, apply trigonometric functions to solve problems related to angles of elevation and depression, periodic motion, and more.

With consistent practice and understanding of the concepts, you can become proficient in using trigonometric functions effectively.

.Study GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.