Definition

Trigonometric ratios are the ratios of the sides of a right-angled triangle. The six trigonometric ratios are sine, cosine, tangent, cosecant, secant, and cotangent, denoted as sin, cos, tan, csc, sec, and cot respectively.

Basic Trigonometric Ratios

For a right-angled triangle with sides a, b, and hypotenuse c, and an angle θ:

Sine (sin θ) = Opposite/Hypotenuse = a/c
Cosine (cos θ) = Adjacent/Hypotenuse = b/c
Tangent (tan θ) = Opposite/Adjacent = a/b

Reciprocal Trigonometric Ratios

The reciprocal trigonometric ratios are the reciprocals of the basic ratios:

Cosecant (csc θ) = 1/Sine = c/a
Secant (sec θ) = 1/Cosine = c/b
Cotangent (cot θ) = 1/Tangent = b/a

Study Guide

To study trigonometric ratios, follow these steps:

Understand the basic definitions and concepts of right-angled triangles and angles.
Memorize the trigonometric ratios and their definitions.
Practice solving problems involving trigonometric ratios, such as finding missing sides or angles in a right-angled triangle.
Learn about the unit circle and how it relates to trigonometric ratios.
Understand the application of trigonometric ratios in real-life situations, such as navigation, engineering, and physics.

Remember to practice regularly and seek help if you encounter difficulties in understanding any concept related to trigonometric ratios.

◂Math Worksheets and Study Guides Sixth Grade. Graphs

Single Line Graph Comprehension

Worksheet/Answer key

Single Line Graph Comprehension

The resources above cover the following skills:

Data Analysis and Probability (NCTM)

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Select and use appropriate statistical methods to analyze data.

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.