Rebecca Wingard-Nelson - Trigonometry Smarts!

Are you having trouble with trigonometry? Do you wish someone could explain this challenging subject in a clear, simple way? From triangles and radians to sine and cosine, this book takes a step-by-step approach to teaching trigonometry. Trigonometry Smarts! provides clear lessons with easy-to-learn techniques and plenty of examples.

About the Author

Rebecca Wingard-Nelson has worked in public, private and home-school mathematics education. She has been involved in various educational math projects, including developing and writing state assessment and proficiency tests, as well as writing and editing text books.

If you were to look up the meaning of the word mathematics, you would find that it is the study of numbers, quantities, and shapes and how they relate to each other.

Mathematics is important to all world cultures, including our world of work. The following are just some of the ways in which studying math will help you:

You will know how much money you are spending.

You will know if the cashier has given you the right amount of change.

You will know how to use measurements to build things.

Your science classes will be easier and more interesting.

You will understand music on a whole new level.

You will be able to qualify for and land a rewarding job.

Trigonometry is a branch of mathematics that studies the measurements of triangles and how their sides and angles relate to each other. Distances that are difficult to measure, such as the distance from the earth to the moon or across a lake, can be found using trigonometry. Sound vibrations and the flow of electrical currents also use applications of trigonometric functions.

This book has been written so that you can learn about trigonometry at your own speed. You can use this book on your own, or work with a friend, tutor, or parent.

Good luck and have fun!

Trigonometry and geometry use words that describe different kinds of lines and angles that are used to make figures.

Lines

A line extends in two directions and does not end. A line is always straight. Arrows are used to show that a figure is a line. Lines are named using two points on the line.

This line is written and is read line AB.

A line segment is part of a line and has two endpoints. This line segment is written and is read line segment CD.

A ray is also part of a line. It has one endpoint but does not end in the other direction. This ray is written and is read ray EF.

Lines, line segments, and rays may cross, or intersect. When they intersect and form a right angle, or square corner, they are called perpendicular. If they do not intersect no matter how far they are extended, they are called parallel.

Line segments that do not cross are not always parallel. They are only parallel if they will never cross, no matter how far they are extended.

Angles

When two lines intersect, angles are formed. These angles will share the same endpoint. The shared endpoint is called the vertex.

Two rays (or line segments) are the sides of each angle. To name an angle, use a point on each ray or line segment and the vertex. The vertex letter must be the middle letter in the name. This angle can be named XYZ, which is read angle XYZ, or ZYX, which is read angle ZYX.

When it will not be confusing, angles may be named using only the vertex. This angle could be called Y, which is read angle Y.

When two lines cross, four angles are formed. All four angles have the same vertex.

Angles can be described by their size. They are measured in units called degrees. The symbol for degrees is .

Measuring Angles

Angles are measured using a protractor. When you use a protractor, place it so that the hole in the center of the straight edge is over the vertex. Align one side of the angle with the line on the protractor that crosses the hole. Read the number where the other side of the angle passes under the protractor.

Right angles are angles like the corner of a square or rectangle. They are labeled with a small corner shape.

Right angles have a measure of exactly 90.

If you do not have a protractor, use an index card to help you decide if an angle is acute, right, obtuse, or straight.

Acute angles are angles that are smaller than right angles.

Straight angles are straight lines.

Obtuse angles are larger than right angles, but smaller than straight angles.

Adding Angles

Angles can be added together to form new angles. Two angles that add up to 90 are called complementary angles.

Two angles that add up to 180 are called supplementary angles.

All complementary angles are acute.

A complete circle has 360.

A triangle has three sides and three angles. You can name a triangle using the symbol for a triangle, , and then listing the vertices of the triangle in any order you choose. This triangle can be named ABC.

The sum of the angles in a triangle is always 180. When you know two of the angle measures in a triangle, you can find the third angle measure.