Sine Cheat Sheet (customizable)

Home > Math Cheat Sheets > Sine Cheat Sheet

To build or customize your cheat sheet (table below) adjust the parameters (From, Step, Decimals) in this form and hit the Update button. *You could also enter the angles (in degrees) to calculate their sine* directly on the table**
From:	Step:	Decimals:

[See also Cosine Cheat Sheet]

[Worksheet]

[Printer friendly]

Sine of an Angle(in Degrees)
[sin(θ)]

sin()	=	0.000000
sin()	=	0.052336
sin()	=	0.104528
sin()	=	0.156434
sin()	=	0.207912
sin()	=	0.258819
sin()	=	0.309017
sin()	=	0.358368
sin()	=	0.406737
sin()	=	0.453990
sin()	=	0.500000
sin()	=	0.544639
sin()	=	0.587785
sin()	=	0.629320
sin()	=	0.669131
sin()	=	0.707107
sin()	=	0.743145
sin()	=	0.777146
sin()	=	0.809017
sin()	=	0.838671
sin()	=	0.866025
sin()	=	0.891007
sin()	=	0.913545
sin()	=	0.933580
sin()	=	0.951057

sin()	=	0.965926
sin()	=	0.978148
sin()	=	0.987688
sin()	=	0.994522
sin()	=	0.998630
sin()	=	1.000000
sin()	=	0.998630
sin()	=	0.994522
sin()	=	0.987688
sin()	=	0.978148
sin()	=	0.965926
sin()	=	0.951057
sin()	=	0.933580
sin()	=	0.913545
sin()	=	0.891007
sin()	=	0.866025
sin()	=	0.838671
sin()	=	0.809017
sin()	=	0.777146
sin()	=	0.743145
sin()	=	0.707107
sin()	=	0.669131
sin()	=	0.629320
sin()	=	0.587785
sin()	=	0.544639

sin()	=	0.500000
sin()	=	0.453990
sin()	=	0.406737
sin()	=	0.358368
sin()	=	0.309017
sin()	=	0.258819
sin()	=	0.207912
sin()	=	0.156434
sin()	=	0.104528
sin()	=	0.052336
sin()	=	0.000000
sin()	=	-0.052336
sin()	=	-0.104528
sin()	=	-0.156434
sin()	=	-0.207912
sin()	=	-0.258819
sin()	=	-0.309017
sin()	=	-0.358368
sin()	=	-0.406737
sin()	=	-0.453990
sin()	=	-0.500000
sin()	=	-0.544639
sin()	=	-0.587785
sin()	=	-0.629320
sin()	=	-0.669131

sin()	=	-0.707107
sin()	=	-0.743145
sin()	=	-0.777146
sin()	=	-0.809017
sin()	=	-0.838671
sin()	=	-0.866025
sin()	=	-0.891007
sin()	=	-0.913545
sin()	=	-0.933580
sin()	=	-0.951057
sin()	=	-0.965926
sin()	=	-0.978148
sin()	=	-0.987688
sin()	=	-0.994522
sin()	=	-0.998630
sin()	=	-1.000000
sin()	=	-0.998630
sin()	=	-0.994522
sin()	=	-0.987688
sin()	=	-0.978148
sin()	=	-0.965926
sin()	=	-0.951057
sin()	=	-0.933580
sin()	=	-0.913545
sin()	=	-0.891007

Customize the style of your Cheat Sheet

Background color for header:
Font color for header:
Background color for odd rows:
Background color for even rows:
Size:	S M L

Exporting the Cheat Sheet to PDF

To export the cheat sheet as a PDF, you can follow these simple steps that leverage the browser's capabilities to save the printer-friendly version of the sheet as a PDF:

Click on the Printer friendly link (here or above the table), or on the Worksheet link if you wanted to get the Worksheet instead of the Cheat Sheet.
Press Ctrl + P (or Cmd + P on Mac) to open the print dialog
In the print dialog, choose Save as PDF as the destination.

The specific steps may vary slightly depending on the browser being used. This enables you to create a portable and accessible version of the cheat sheet that you can refer to anytime, anywhere.

What Is the Sine of an Angle?

The sine of an angle is a concept from trigonometry, a branch of mathematics that deals with the relationships between the angles and sides of triangles. To understand it, let's break it down into simple steps:

Right Triangle Basics

Imagine you have a right triangle, which is a triangle with one angle that is exactly 90 degrees. The side opposite the 90-degree angle is called the hypotenuse. The other two sides are called the adjacent and opposite sides, depending on which angle you're focusing on.

Understanding the Sine Function

For any angle in a right triangle, the sine of that angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In a formula, it looks like this:

Sine of an angle(sin θ) = (Opposite Side) / (Hypotenuse)

Example

Let's say you have a right triangle where:

The angle you're interested in is 30 degrees.
The length of the side opposite this angle is 1 unit.
The length of the hypotenuse is 2 units.

Then, the sine of 30 degrees would be:

sin(30°) = 1 / 2 = 0.5

This means that for a 30-degree angle, the opposite side is half the length of the hypotenuse.

Why is it Useful?

The sine function helps you find unknown side lengths of triangles when you know some of the angles or other sides. It's also foundational in understanding waves, circles, and oscillations in more advanced math and physics.

Think of a ladder leaning against a wall. If you know the angle the ladder makes with the ground and the length of the ladder (the hypotenuse), you can use the sine function to find out how high up the wall the ladder reaches.

This is the basic idea of the sine of an angle-it's just a ratio that helps us understand the relationship between the sides of a right triangle.