CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II.1. sin 83° A. 88.09084757°2. B. 63.25631605°3. C. 1.909152433°4. D. 17.45760312°5. E. 0.28674538586. F. 1.9626105067. G. 14.47751219°8. H. 1.0154266129. I. 1.05146222410. J. 0.9925461516

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insert step 1: Identify the trigonometric function in Column I, which is sin 83°.

insert step 2: Recall that the sine function gives the ratio of the opposite side to the hypotenuse in a right triangle.

insert step 3: Use a calculator or trigonometric table to find the approximate value of sin 83°.

insert step 4: Compare the calculated value of sin 83° with the approximations given in Column II.

insert step 5: Match sin 83° with the closest approximation from Column II, which is likely to be a value close to 1.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. For example, the sine function of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse. Understanding these functions is crucial for solving problems involving angles and their corresponding values.

Angle Measurement

Angles in trigonometry can be measured in degrees or radians. In this context, degrees are used, where a full circle is 360 degrees. Knowing how to convert between degrees and radians, as well as how to interpret angle measures, is essential for accurately matching trigonometric function values with their corresponding angles.

Approximation of Trigonometric Values

Trigonometric values can be approximated using calculators or trigonometric tables. For instance, the sine of 83° can be approximated to a decimal value, which is necessary for matching with the provided options. Familiarity with how to find and interpret these approximations is key to solving the matching problem presented.

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