Question

In $3-44,$ find the exact value. $$ \cos 60^{\circ} $$

   In $3-44,$ find the exact value.
$$
\cos 60^{\circ}
$$

Algebra 2 and Trigonometry

Algebra 2 and Trigonometry

Ann Xavier Gantert 1st Edition

Chapter 9, Problem 8

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Solved by Expert Anthony Pisaturo

08/08/2019

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The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. It is often used in trigonometry to define the trigonometric functions of angles. Show more…

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In $3-44,$ find the exact value. $$ \cos 60^{\circ} $$

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Key Concepts

Exact Value

An exact value refers to the precise expression of a trigonometric function’s output, typically presented in a simplified fractional or radical form. Unlike decimal approximations, exact values maintain mathematical precision, which is especially important in proofs and symbolic computations involving trigonometric functions.

Cosine Function

The cosine function is one of the primary trigonometric functions. It relates an angle in a right triangle to the ratio of the adjacent side's length to the hypotenuse. When extended to the unit circle, cosine measures the x-coordinate of a point corresponding to a given angle, making it a fundamental concept for understanding rotations and oscillatory behavior in mathematics.

Standard Angles

Standard angles are specific angle measures (such as 0°, 30°, 45°, 60°, and 90°) whose trigonometric values can be determined exactly using simple geometric constructions or right triangles. These angles serve as benchmarks in trigonometry, allowing for the precise calculation and comprehension of sine, cosine, and tangent values without relying on numerical approximations.

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