Trigonometry Study Guide

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the study of the relationships between the angles and sides of triangles. It is used to solve problems involving right-angled triangles and has numerous applications in various fields such as physics, engineering, and astronomy.

Basic Trigonometric Functions

There are six basic trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. These functions are defined in terms of the sides of a right-angled triangle.

Sine (sin θ): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos θ): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan θ): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Cosecant (csc θ): The reciprocal of the sine function.
Secant (sec θ): The reciprocal of the cosine function.
Cotangent (cot θ): The reciprocal of the tangent function.

Trigonometric Identities

Trigonometric identities are equations that are true for all values of the variables within their domains. Some of the fundamental trigonometric identities include:

Pythagorean Identities: sin²θ + cos²θ = 1 and 1 + tan²θ = sec²θ
Reciprocal Identities: csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
Quotient Identities: tan θ = sin θ / cos θ, cot θ = cos θ / sin θ

Applications of Trigonometry

Trigonometry has numerous real-world applications, including:

Calculating distances and heights using angles and known lengths
Modeling periodic phenomena such as sound and light waves
Solving navigation problems in geography and astronomy
Engineering and construction for measuring and designing structures

Study Tips for Trigonometry

Here are some tips to help you study and understand trigonometry:

Practice drawing and solving right-angled triangles to understand the relationships between angles and sides.
Memorize the basic trigonometric functions and their definitions.
Work through plenty of practice problems to reinforce your understanding of trigonometric concepts and identities.
Use trigonometric tables and calculators to verify your calculations and familiarize yourself with trigonometric values.
Apply trigonometry to real-world problems to see its practical significance and develop a deeper understanding of its applications.

By understanding the basic trigonometric functions, identities, and their applications, you can develop a strong foundation in trigonometry and apply it to various mathematical and real-world problems.

◂Math Worksheets and Study Guides Fifth Grade. Order of Operations

The resources above cover the following skills:

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 5 Focal Points (NCTM)

Algebra: Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities. They create graphs of simple equations. They explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations.