Cos 0

Bookmark added to your notes.
View Notes

Cos 0 Degree Value

Cos 0 equals to 1 (Cos 0 = 1). In other words, the value of Cos 0 is 1. Now, the question is how the value of Cos 0 has been derived. The value can be determined through the usage of quadrants of a unit circle. The process is discussed in the following section.

As you already know, trigonometric functions refer to angular functions that relate the angles of a triangle. For studying periodic phenomena of light and sound waves, trigonometric functions have been used. These functions are also crucial for studying the harmonic oscillation and average temperature variations.

Formula to Find Cos

The cosine function of an angle follows a particular formula. According to this formula, the value of a cosine function of an angle is the length of the adjacent side divided by the length of the hypotenuse side. The formula is written below.

Cos X = \[\frac{\text{Adjacent Side}}{\text{Hypotenuse Side}}\]

How to Find the Value of Cos 0?

There are three basic trigonometric ratios, and they are sine function, cosine function, and tangent function. With the help of the sin, cos, and tan functions, the angles of a triangle can be calculated.

For understanding the cosine function of an acute angle, you need to draw a right-angled triangle on a piece of paper. The triangle obviously has three sides, and these sides can be defined in the following way:

  • Choose an angle of the triangle, and the opposite side of the chosen angle will be called the “opposite side”.

  • The side of the triangle placed opposite to the right angle has been called “hypotenuse side”. Notably, this is the longest side of a right-angle triangle.

  • Finally, the “adjacent side” refers to the remaining side of the triangle.

Determining Value of Cos 0 with Unit Circle

Using a unit circle, “Cos 0” value can be derived. The process starts with assuming a unit circle which shares its center with the origin of the coordinate axes.

What is Cos 0  ?

The value of the cosine in the 0° right triangle is known as the cosine of angle 0°. The cosine of angle 0° is a value, which denotes the remainder of length of adjacent side to the length of hypotenuse if the angle of a right triangle is equivalent to 0°. 

under the Sexagesimal system, the cos of zero degree angle is mathematically expressed as cos 0° and the exact value of cosine of angle 0° = 1 . Thus, mathematically it is written in the following form in trigonometry i.e cos 0° = 1 

We can also express the cosine of angle zero degrees in two other forms under trigonometric mathematics ie. circular system and centesimal system. 

Cos 0 in  Circular System

In a circular system, the cosine of zero degrees is mathematically represented as the cosine of zero radian. It is written in the following form in circular system cos (0) =1 

Cos 0 in  Centesimal System

Similarly, In a centesimal system, the cosine of zero degrees is mathematically represented as the cosine of zero degree grades. It is written in the following form in centesimal system cos (0^9) =1 

FAQ (Frequently Asked Questions)

Q1. What is the Value of Cos 0?

Answer:  cos 0° is equal to √ (4/4) = 1. The standard angles such as cos 0°, 30°, 45°, 60° and 90° are all possibly the positive roots of their fractional values.

Q2. How Can We Remember Cos Value?

Answer: Here is a quick trick to remember the values of the cos 0 degrees. Just remember cos goes in a reverse direction like "3,2,1". That being said, the value for various degrees of cos goes like this:

 cos(30°)  =√3/2

 cos(45°)  = √2/2 

 cos(60°)  =√1/2  

cos 90° = √(0/4) = 0

Now that we are aware of the sin and cos value of the standard angles, thus we are easily able to find the values of the other trigonometric ratios of the standard angles.

Q3. What is a Trigonometric Table and its Importance?

Answer:  The Trigonometrical ratios table will significantly enable you to identify the values of trigonometric standard angles of various trigonometric ratios such as 0°, 30°, 45°, 60° and 90°.

The values of trigonometric ratios of standard angles play a significant role when it comes to solving the trigonometric problems. Hence, it becomes essential for the students to remember the value of these standard angles of the trigonometric ratios.

Q4. What is the Value of Cosine of the Standard Angles?

Answer:  First, you need to remember to not get confused between cos and cosine. Both are different trigonometric angles. Thus, find below the the standard angles of cosine 0°, 30°, 45°, 60° and 90° which are:

  • csc 0 degrees = not defined.

  • csc 30 degrees = 2

  • csc 45 degrees = √2

  • csc 60 degrees = 2√3/3

  • csc 90 degrees = 1.