# Solve Algebraic Problems

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Let's try θ = 30°: sin(−30°) = −0.5 and −sin(30°) = −0.5 So it is true for θ = 30° Let's try θ = 90°: sin(−90°) = −1 and −sin(90°) = −1 So it is also true for θ = 90° Is it true for all values of θ?

Solving Algebra word problems is useful in helping you to solve earthly problems.

The examples of correspondences we have given involve two sets X and Y.

In our first example, X denotes the set of books in a library and Y the set of positive integers.

Beginning students are sometimes confused by the symbols f and f(x). Two functions f and g from X to Y are said to be equal, written for every x in X.

Example 1 Let f be the function with domain R such that f(x) = x, where a is a real number.

We sometimes represent correspondences by diagrams of the type shown in Figure 1.17, where the sets X and Y are represented by points within regions in a plane. However, the same element of Y may correspond to different elements of X.

The curved arrow indicates that the element y of Y corresponds to the element x of X. For example, two different books may have the same number of pages, two different people may have the same birthday, and so on.

After all, you wouldn’t want a surgeon to crack your ribs and perform a heart transplant without first identifying the source of your chest pains. Now that you understand the word problem’s purpose, determine the answer’s unit.

For example, will the answer be in miles, feet, ounces, pesos, dollars, the number of trees, or a number of televisions?

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