Visual Glossary By: Anya Khosla Unit 6

Introduction Most people in this world know how to read. Everywhere you go, people are always reading. From s on their smartphones to books, people are reading. But what is reading without knowing what the words mean?! If you don’t know what anything means, you won’t be able to understand anything. To look up words, people use dictionaries. This power point is like a dictionary, but on math concepts. These terms which you are about to see are important terms which will help you understand unit 6 (unit 6 being the “book”). I chose these terms because work in unit 6 will be easier if these terms are known. They are the need-to-know terms so that you understand the unit. By knowing the definition of these terms, solving problems in this unit will be easier. If word problems give you the values of one of these terms (ex. Angle of elevation), you will know exactly where that value is located when drawing the diagram. They can help create equations which are needed to solve the problem.

LESSON 1

Dilation To enlarge or reduce a figure by a certain amount (scale factor) When the original figure is dilated, the figure can either get bigger or smaller. In this example, it got smaller. The side lengths have to be reduced (in this case) by the same amount to get the smaller dilated figure. The original sides have to be dilated by a fraction to get a smaller dilated figure.

Scale Factor How much the figure is enlarged or reduced by The scale factor is the number in which the sides are enlarged or reduced by. As stated in the previous slide, to get a reduced figure you have to have a scale factor that is a fraction. To get an enlarged figure, the scale factor is going to be a whole number greater then 1.

LESSON 4

Geometric Mean The geometric mean of two positive numbers is the positive square root of the product of those two numbers. The geometric mean is used to find ratios between two sides in a right triangle (trigonometric ratio). The ratios of the sides are the geometric means of those two sides.

LESSON 5

Trigonometric Ratio The ratio of two sides of a right triangle Three different types of trigonometric ratios are sine, cosine, and tangent of an angle. To find the sine, cosine, or tangent of an angle, a ratio between two sides of the right triangle will always have to be created. That ratio between the two sides is the trigonometric ratio.

Sine The sine of an angle is the ratio of the leg opposite the angle to the length of the hypotenuse To find the sine of an angle, you have to create a Trigonometric ratio. You always have to make sure that the mode on the calculator is in “degree mode” or else you won’t get the sine of the angle. Since an angle is measured in degrees, the Sine has to be in degrees also because we are finding the Sine of the angle.

Cosine The cosine of an angle is the ratio of the leg adjacent the angle to the length of the hypotenuse To find the cosine of an angle, you have to create a Trigonometric ratio. You always have to make sure that the mode on the calculator is in “degree mode” or else you won’t get the cosine of the angle. Since an angle is measured in degrees, the cosine has to be in degrees also because we are finding the cosine of the angle.

Tangent The tangent of an angle is the ratio of the leg opposite the angle to the length of the leg adjacent to the angle. To find the tangent of an angle, you have to create a Trigonometric ratio. You always have to make sure that the mode on the calculator is in “degree mode” or else you won’t get the tangent of the angle. Since an angle is measured in degrees, the tangent has to be in degrees also because we are finding the tangent of the angle.

LESSON 6

Angle of elevation The angle formed by a horizontal line and a line of sight above the line. In the diagram on the right, the base angle next to the 90 degree angle is the angle of elevation because it’s the angle formed by a horizontal line (the base) and the line of sight (the sun). The angle is above the base line, making it an elevation.

Angle of depression The angle formed by a horizontal line and a line of sight to a point below the line. In the diagram on the right, the top angle is the angle of depression. Imagine an imaginary horizontal line, parallel to the base, running from the sun. The angle is under the Imaginary horizontal line, making it an angle of Depression.