## + (855) 550-0571

POTENTIAL AND CREATIVITY
WITH A FREE TRIAL CLASS
DEVELOP TECHNICAL, SOFT, &
ENTREPRENEURIAL SKILLS
AGE 7-16 YEARS
CARD BY ATTENDING A FREE TRIAL CLASS
BOOK A FREE TRIAL

# What is cos 5pi 6?

## |

### 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!

Recommended Reading: NAVIGATING THE WORLD OF MATRIX MATH PROBLEMS

### Method 1: The Unit Circle Approach

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

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.

Recommended Reading: WHAT IS 9/16 AS A DECIMAL?

### 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.

Moonpreneur understands the needs and demands this rapidly changing technological world is bringing with it for our kids. Our expert-designed Advanced Math course and Math Quiz for grades 3rd, 4th, 5th, and 6th will help your child develop math skills with hands-on lessons, excite them to learn, and help them build real-life applications.

Register for a free 60-minute Advanced Math Workshop today!

## 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.

#### Moonpreneur

Moonpreneur is an ed-tech company that imparts tech entrepreneurship to children aged 6 to 15. Its flagship offering, the Innovator Program, offers students a holistic learning experience that blends Technical Skills, Power Skills, and Entrepreneurial Skills with streams such as Robotics, Game Development, App Development, Advanced Math, Scratch Coding, and Book Writing & Publishing.
Subscribe
Notify of

Inline Feedbacks

## MOST POPULAR

### Alibaba Global Mathematics Competition

JOIN A FREE TRIAL CLASS

### MATH QUIZ FOR KIDS - TEST YOUR KNOWLEDGE

Start The Quiz