CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.

tan 45°

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Identify the trigonometric function given explicitly: tan 45°. Recall that tan 45° equals 1, so match tan 45° with value B (1).

Recall the common exact values of sine, cosine, and tangent for special angles such as 30°, 45°, and 60°. For example, sin 30° = 1/2, cos 60° = 1/2, sin 45° = cos 45° = √2/2, tan 60° = √3, and so on.

Match each trigonometric function from Column I with its corresponding exact value from Column II by comparing the known values. For instance, if you see sin 30°, match it with C (1/2); if you see cos 45°, match it with H (√2/2).

Use the Pythagorean identities and reciprocal relationships if needed to confirm matches. For example, since tan θ = sin θ / cos θ, if you know sin and cos values, you can find tan values to help with matching.

Double-check that each value from Column II is used appropriately according to the function's known exact values, and ensure no mismatches or contradictions occur.

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주요 개념

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Basic Trigonometric Ratios

Trigonometric functions such as sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. For example, tan 45° equals 1 because the opposite and adjacent sides are equal. Understanding these fundamental ratios is essential for matching functions to their values.

Special Angles and Their Values

Certain angles like 30°, 45°, and 60° have well-known exact trigonometric values involving square roots and fractions. Memorizing these special angle values, such as sin 30° = ½ or cos 60° = ½, helps quickly identify correct matches without calculation.

Simplification of Radical Expressions

Trigonometric values often involve radicals like √2 or √3, sometimes divided by integers. Being able to simplify and recognize equivalent radical expressions, such as √3/2 or 2√3/3, is crucial for correctly matching the function values given in different forms.

CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all. tan 45°