What is the Value of Cos(π/4)? - Comprehensive Guide

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Overview

Cos(π/4) is a mathematical concept referring to the angle of a right triangle in which the hypotenuse is 2 units in length and the adjacent side is 1 unit long. This angle is also known as a quarter-turn or 45 degrees. In trigonometry, the cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. The value of cos(π/4) is equal to 0.70710678118.

Step by Step Solution

Determine the angle of the triangle using the law of cosines, that is `cos(x) = adjacent side/hypotenuse`.

Compute the cosine of the angle to get the value for x. In this case, the angle is `π/4` radians or 45 degrees, so you can use the equation `cos(π/4) = adjacent/hypotenuse`.

Find the length of the adjacent side, which is one. So the equation becomes `cos(π/4) = 1/2`.

1. Finally, the value of cos(π/4) is equal to 0.70710678118.

FAQs

What is the Unit for Cos(π/4)?

The unit for the cosine function is radians. Therefore, when computing the value of cos(π/4), the answer is given in radians.

What is the Range of Values for Cos(π/4)?

The range of values for cos(π/4) is between -1 and 1. Therefore, the value of cos(π/4) is equal to 0.70710678118.

Is cos(π/4) Equal to sqrt(2)?

Yes, the value of cos(π/4) is equal to the square root of 2. Therefore, cos(π/4)  is equal to 0.70710678118.

How Do You Find the Value of Cos(π/4)?

1. Determine the angle of the triangle using the law of cosines, that is `cos(x) = adjacent side/hypotenuse`.
2. Compute the cosine of the angle to get the value for x.
3. Find the length of the adjacent side, which is one.
4. Finally, the value of cos(π/4) is equal to 0.70710678118.

How Does Knowing the Value of Cos(π/4) Help?

Knowing the value of cos(π/4) can help with various tasks, such as finding the sin, cos, and tan of every angle, computing the area of a triangle or circle, and solving any trigonometric equation. In addition, knowing the value of cos(π/4) can also help solve physics, engineering, and other applied mathematics problems.

Resources

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