What is cos 5pi 6?

Updated: January 9, 2024

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Category: Advanced Math

Introduction:

This one is from trigonometry.

The trigonometric function cosine, denoted as cos, plays a significant role in mathematics and science. But what happens when you’re faced with cos(5π/6) and need to find its value? In this blog, we’ll learn to calculate cos(5π/6) with two methods. Let’s start!

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Method 1: The Unit Circle Approach

$What is cos 5pi 6?$

One of the most intuitive ways to find the value of cos(5π/6) is by using the unit circle. The unit circle is a circle with a radius of 1, centered at the origin (0, 0) on a Cartesian plane.

Step 1: Locate the angle

Start by locating the angle 5π/6 on the unit circle. This angle falls in the second quadrant.

Step 2: Find the coordinates

In the second quadrant, the x-coordinate of the point where the angle intersects the unit circle will be negative. Therefore, cos(5π/6) is equal to -√3/2.

Method 2: The Reference Angle Approach

$What is cos 5pi 6?$

Another method to determine cos(5π/6) involves finding its reference angle, which is the acute angle formed between the terminal side of the given angle and the x-axis.

Step 1: Find the reference angle

Calculate the reference angle for 5π/6 by subtracting it from π (180 degrees). In this case, the reference angle is π – 5π/6 = π/6.

Step 2: Use the reference angle

Since cos(π/6) is a well-known value (equal to √3/2), cos(5π/6) will have the same absolute value but with the opposite sign. Therefore, cos(5π/6) = -√3/2.

Example:

Find cos(5π/6).

Using the unit circle, locate the angle in the second quadrant. The x-coordinate is -√3/2.
Therefore, cos(5π/6) = -√3/2.

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Conclusion:

Calculating trigonometric functions like cos(5π/6) can be straightforward when using the unit circle or reference angles. By understanding these methods and concepts, you can easily find cosine values for various angles and solve trigonometric problems.

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Frequently Asked Questions

Q1: What is the cosine function?

The cosine function (cos) is a trigonometric function that relates the ratio of the adjacent side to the hypotenuse in a right triangle. It is widely used in mathematics, physics, engineering, and various other fields.

Q2: What are reference angles?

Reference angles are acute angles formed between the terminal side of a given angle and the x-axis. They are used to simplify trigonometric calculations and find trigonometric function values for angles in different quadrants.

Q3: Why is cos(5π/6) equal to -√3/2?

Cos(5π/6) is negative because it falls in the second quadrant of the unit circle, where the x-coordinate is negative. The value -√3/2 represents the x-coordinate of the point where the angle 5π/6 intersects the unit circle.

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