Question

Find the exact function value. $$\sin 45^{\circ}$$

   Find the exact function value.
$$\sin 45^{\circ}$$

Algebra and Trigonometry

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 6, Problem 20

Instant Answer

Solved by Expert Ankit Gupta

07/02/2020

Step 1

Step 1: First, we need to understand that the sine function gives the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Show more…

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Find the exact function value. $$\sin 45^{\circ}$$

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Key Concepts

Exact Trigonometric Values

Exact trigonometric values involve evaluating trigonometric functions at key angles with expressions comprising radicals and fractions instead of decimal approximations. This concept is important for solving problems with precision in both theoretical and applied mathematics, providing clarity and exactness in calculation.

Special Triangles

Special triangles, such as the 45-45-90 triangle, are crucial in trigonometry because they provide exact values for trigonometric functions at specific angles. The 45-45-90 triangle, in particular, has equal legs, which leads to simple ratios that allow for the derivation of exact expressions like sin 45° = ?2/2.

Sine Function

The sine function is a fundamental trigonometric function that, in a right-angled triangle, represents the ratio of the length of the side opposite a given angle to the length of the hypotenuse. It is also interpreted as the y-coordinate of a point on the unit circle corresponding to a given angle, making it essential in understanding periodic phenomena and oscillatory behavior.

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