sin A

Scan Quick Response Code In Objective-CUsing Barcode Control SDK for iPhone Control to generate, create, read, scan barcode image in iPhone applications.

Create QR-Code In Objective-CUsing Barcode encoder for iPhone Control to generate, create QR Code ISO/IEC18004 image in iPhone applications.

Inverses of Sine, Cosine, and Tangent

Decoding Quick Response Code In Objective-CUsing Barcode decoder for iPhone Control to read, scan read, scan image in iPhone applications.

Bar Code Drawer In Objective-CUsing Barcode generation for iPhone Control to generate, create bar code image in iPhone applications.

The inverses of sine, cosine, and tangent allow you to do the reverse of the sine, cosine, and tangent functions and find the angle The trigonometric functions and their inverses are as follows: Trigonometric Function y y y sin x cos x tan x x x x sin cos tan

Make Denso QR Bar Code In Visual C#Using Barcode maker for VS .NET Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications.

Printing QR Code ISO/IEC18004 In .NETUsing Barcode drawer for ASP.NET Control to generate, create QR Code image in ASP.NET applications.

1y 1y 1x

Generate QR In Visual Studio .NETUsing Barcode encoder for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications.

Painting QR Code ISO/IEC18004 In Visual Basic .NETUsing Barcode generation for .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications.

Inverse or x or x or x arc sin y arc cos y arc tan y

Drawing Barcode In Objective-CUsing Barcode creator for iPhone Control to generate, create barcode image in iPhone applications.

Data Matrix Generation In Objective-CUsing Barcode generator for iPhone Control to generate, create ECC200 image in iPhone applications.

Graphs of Trigonometric Functions

Bar Code Encoder In Objective-CUsing Barcode generation for iPhone Control to generate, create barcode image in iPhone applications.

Encode Code 128 Code Set B In Objective-CUsing Barcode creation for iPhone Control to generate, create Code 128C image in iPhone applications.

The sine function, y sin x, and the cosine function, y cos x are periodic functions The period for each function is 2 x can be any real number y is any real numbers between 1 and 1, inclusive

Encode Universal Product Code Version E In Objective-CUsing Barcode encoder for iPhone Control to generate, create UPC-E Supplement 5 image in iPhone applications.

Paint Bar Code In NoneUsing Barcode maker for Software Control to generate, create barcode image in Software applications.

y sin x

UPC-A Supplement 5 Maker In NoneUsing Barcode generator for Font Control to generate, create UPC A image in Font applications.

Reading Barcode In NoneUsing Barcode scanner for Software Control to read, scan read, scan image in Software applications.

cos x

UCC - 12 Printer In JavaUsing Barcode maker for Java Control to generate, create UPC Code image in Java applications.

ANSI/AIM Code 39 Decoder In Visual Basic .NETUsing Barcode reader for .NET framework Control to read, scan read, scan image in .NET applications.

Appendix A

Barcode Drawer In JavaUsing Barcode creator for Java Control to generate, create barcode image in Java applications.

EAN / UCC - 13 Maker In NoneUsing Barcode encoder for Microsoft Excel Control to generate, create EAN128 image in Microsoft Excel applications.

Math Handbook

IX Logarithms

Math Handbook

Logarithms with Base b

Let b and x be positive integers, b 1 The logarithm of x with base b, written logb x, equals y, where y is the exponent that makes the equation by x true The log to the base b of x is the number to which you can raise b to get x logb x y if and only if b y x Memory aid: the log is the exponent Examples: Calculate the following logarithms log2

1 16

1 16

Because 2

log10 1000

Because 10 3

When you want to find the log of a number, you also can use a calculator Connecting Math to Physics Physicists use logarithms to work with measurements that extend over several orders of magnitude, or powers of 10 Geophysicists use the Richter scale, a logarithmic scale that allows them to rate earthquakes from 0 to 7, or larger, though the power of earthquakes differ by 7 or more powers of 10

Common Logarithms

Base 10 logarithms are called common logarithms They often are written without the subscript 10 log10 x log x x 0

Antilogarithms or Inverse Logarithms

An antilogarithm is the inverse of a logarithm An antilogarithm is the number which has a given logarithm Example: Solve log x log x x 4 10 4 4 for x

104 is the antilogarithm of 4

Connecting Math to Physics An equation for loudness, L, in decibels, is L 10 log10 R, where R is the relative intensity of the sound Calculate R for a fireworks display with a loudness of 130 decibels 130 13 R 10 log10 R log10 R 1013

Divide by 10 Use logarithm rule

When you know the logarithm of a number and want to know the number itself, use a calculator to find the antilogarithm

20 Write in exponential form log3 81 21 Write in logarithmic form 10 22 Find x log x

4 0001

Math Handbook

1

1 The density, , of an object is given by the ratio of the object s mass, m, and volume, V, according to the equation m/V What is the density of a cube that is 12 cm on each side and has a mass of 256 g 2 An object that is moving in a straight line with speed v covers a distance, d vt, in time t Rewrite the equation to find t in terms of d and v How long does it take a plane that is traveling at 350 km/h to travel 1750 km 3 Convert 523 kg to milligrams 4 The liquid measure milliliter, mL, is the same as 1 cm3 How many milliliters of liquid can be held in a 25-m3 container 5 Part of the label from a vitamin container is shown below The abbreviation mcg stands for micrograms Convert the values to milligrams

7 How many significant digits are there in each of the following measurements a 100 m b 00023 m/s c 1001 m d 20023 8 The buoyant (upward) force exerted by water on a submerged object is given by Vg, where is the the formula F density of water (10 103 kg/m3), V is the volume of the object in m3, and g is the acceleration due to gravity (980 m/s2) The force is in newtons Rewrite the equation to find V in terms of F Use this to find the volume of a submerged barrel if the buoyant force on it is 9200 N 9 What is 23 kg 023 g 10 Solve the following problems a 155 cm 121 cm b