Question

Match the trigonometric function values. $$ \sin 45^{\circ} $$

   Match the trigonometric function values.
$$
\sin 45^{\circ}
$$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 6, Problem 37

Instant Answer

Solved by Expert Rahul Mittal

06/20/2021

Step 1

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

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Match the trigonometric function values. $$ \sin 45^{\circ} $$

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Key Concepts

Unit Circle

The unit circle is a fundamental concept in trigonometry where a circle of radius one is used to define trigonometric functions for all real angles. By interpreting angles on the unit circle, one can understand the behavior and properties of sine and cosine functions, facilitating the computation of exact values for standard angles.

Special Right Triangles

Special right triangles, like the 45-45-90 triangle and the 30-60-90 triangle, have side ratios that allow for the easy determination of trigonometric function values for the angles involved. Their predictable ratios provide a quick and precise method to derive sine, cosine, and tangent values without resorting to numerical approximations.

Sine Function

The sine function, one of the primary trigonometric functions, is typically defined in a right triangle as the ratio of the length of the side opposite an angle to the length of the hypotenuse. In the context of the unit circle, sine corresponds to the y-coordinate of a point on the circle where the terminal side of the angle intersects.

Special Angles

Special angles, such as 30°, 45°, and 60°, are particularly important in trigonometry because they produce exact values for trigonometric functions. These angles simplify calculations and are frequently used in various applications, from solving geometric problems to analyzing periodic phenomena.

Trigonometry

Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles. It introduces functions that describe these relationships, such as sine, cosine, and tangent, which are essential in various fields like physics, engineering, and computer science.

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