What is cos30 degree in trigonometry?

(Last Updated On: July 12, 2023)

What is cos30 degree? In trigonometry, the cosine function can be defined by the proportion of the adjacent side in relation to the hypotenuse. When the angle of the right triangle is 30 degrees, the cosine value for that angle, i.e., that of Cos 30 degree is given in the form of a fraction, 3/2. It is important to note that sec 30 is reciprocal to the Cos Value 30.

cos30 degree

Cos 30 Value

Cos 30 degrees can be known as cos 30deg. It has a value in fractional form, which is 3/2.

Cos 30deg = 3/2

Cos 30 degree =3/2 is an unreal number equal to 0.8660254037 (decimal format).

Thus, the exact amount of 30 ° is listed as 0.8660 approx.

3/2 is the amount of cos30 degree, which is a trigonometric proportion or trigonometric value of an angle.

Cos 30

A different alternative to cos30 degree would be pi/6, the p/6 form of Cos 33 ( 1/3 ) g

Trigonometric ratio3 / 20.8660254037
Circular systempi/6 or pi/6 or0.8660254037
Centesimal systemCos 33 ( 1/3 )g0.8660254037

 Cos 30 Degrees Proof

Now that you have the importance of the cos30 degree Let’s find out how to determine this value.

We will examine two methods to draw it.

  1. Theoretical approach
  2. Practical method

An approach to theoretical aspects

Understanding that the length of the opposite side is half that of its hypotenuse Right Triangle property applies to angles of 30 degrees in the right triangle given.

Since we have two sides, which are long on the other side and the hypotenuse, ,that third is unknown, i.e., the adjacent side. We have to discover this site to determine Cos 30 degrees. Cos 30, which is 30°.

Which COS value is 1?


Is COS-1?

Standard Notation cos-1(x) can refer to the reverse of cosine. It is also known as “arccosine” and can be written as arcos (x) or on various calculators cos (x). Similar to the inverse sine, reverse tangent, and other similar terms.

What is COS-1 utilized to do?

The inverse trigonometric functions sin-1(x), cos-1(x), and tan-1(x) can be used to determine the measurement of the angle of right triangles when two side lengths are identified.

What exactly is Cos Square theta?

Answer: The cosine double angle formula is cos(2theta)=cos2(theta) – sin2(theta). Cosine squared plus sin squared equals one could be written as cosine squared theta = 1 minus sine squared theta, or sine squared Theta is one less cosine squared theta equals one minus cosine squared.

The alternative version of Cos 30

In math, there’s another way to write the cos30 degree, which will be cos(/6) (2 equals 360°. So, = 180 degrees. /6 = 180deg/6 =30deg) within the circulatory system. It is also described by cos(33 ) for the centesimal systems. The difference between cos(/6) along with cos(33 ) is 3-232.

Proof for Cos 30 Degrees

It is essential in math to be able to accurately calculate a number with a variety of methods to be able to consider it a given. It is possible to determine the value for cos 30, which could be determined through the use of theoretical and practical techniques. These are the mathematical methods for determining how much a cos30 degree is worth and a trigonometric method that is a possibility.

Using the Theoretical Approach

In any right-angle triangle, a straight and established relationship exists between the sides when the angle is set at 30 degrees. We may try to apply this Pythagorean theorem to calculate how much value the side is adjacent to it. In all cases, the length on the other side is equal to half that of the hypotenuse. Therefore, we can determine the significance of two sides, the hypotenuse as well as the opposite side of the hypotenuse.

Using the Practical Approach

Another method to calculate the worth of cos30 degree is by using the more practical method. Take these actions:

Make a mark at a specific point, such as P, and draw horizontal lines across it.

With a protractor, create a 30-degree angle using P in the middle.

Make a line with an angle ruler to create the angle.

Make an arc by using a compass over that line at any length. Name this point.

At the point of Q, Draw a perpendicular line towards the base. Mark the point where it joins with the bottom at R.

The right-angled triangle is drawn, and the cos30-degree value is known.

Using the Trigonometric Approach

With the help of the cos square concept in trigonometry, i.e., cos2th = sin2th – 1, We can calculate exactly the value for cos(33 ). To calculate the value for cos(/6), we need to replace it with the values of sin(30deg) within that same formula.

cos(30deg) = 1 – sin230deg

The sin30deg value will be 1 (Trigonometric Ratios)

cos(30deg) = 1 – (1/2)2

cos(30deg) = 1 – (1/4)

cos(30deg) = (1 * 4 – 1)/4

cos(30deg) = (4 – 1)/4

cos(30deg) = 3/4

Therefore, cos30 degree = 3/2


Utilizing the trigonometric and geometrical methods(theoretical and practical methods), we have proven that the value of cosp6cosp6 can be found to be 3-232 in the format of fractions, in the fraction format and 0.8660254037 ……, in the decimal format. This gives an approximate value of 0.866.

In addition, we have demonstrated that using the practical approach to the geometrical method using the geometrical method, cos30 degree’s value cos(30deg) is the same as 0.8666666666. Then, you can look at both the results for cos(30deg) and see that cos(30deg) calculated using the method of practice differs from the values obtained by using the methodological methods of the geometrical and trigonometric methods. However, the value of approximately cosp6cosp6 is the same for every case.


What is the exact amount of cos30 degrees?

0.8660 approximately

Cos 30deg = 3/2

So, the exact amount of cos30 degree is described as approximately 0.8660. 3/2 is the number for Cos 30deg, a trigonometric ratio or trigonometric value of an angle.

How do you determine the sin and cos of 30 °?

The result is that sin 30deg = cos60deg = 1/2 as well as sin 60deg = cos 30deg = 3/ 2.

Is cos30 degree positive?

Note: As 30deg is in the 1st quadrant, Cos 30deg’s final result will have a positive value.

How much is COS 30 in terms of fractions?

In the format of fractions, the fraction format, cos(30deg), is equivalent to 0.8660254037. 0.8660254037.

What is the cos30 degree value in radians?

To convert degrees into Radians, multiply p180deg by 180 degree, as an entire circle is 360deg or 2p radians. What is the exact number of cos30 degrees that will be 32?

What is the sin 30 fraction?

1/ 2

Thus, Sin 30 degrees equals an amount that is fractional to 1 2

What triangle has a 30-degree angle?

30-60-90 triangle is a 30–60-90 triangular is a unique right-hand triangle (a right triangle is any triangle with 90 degrees) which always contains angle angles that are 30°, 60°, or 90 degrees.

Can a triangle have two angles of 30 degrees?

A triangle with an equilateral form has three sides and three angles of equal length. Each angle measures 60 degrees. When the length of an equilateral triangular triangle is traced to the bottom of the triangle, Two 90-degree angles form, and the angle at the top is divided into two angles of 30 degrees.