from a handpicked tutor in LIVE 1-to-1 classes
2 Radians to Degrees
Before going to see what is 2 radians to degrees, let us recall a few basics. We have two units used to measure an angle: radians and degrees. 1 radian is the angle made by an arc of a circle whose length is equal to that of its radius. 1 degree is one out of 360 parts when the complete angle at the center of a circle is divided into 360 parts. An angle can be converted from radians to degrees using a formula. Using that formula, 2 radians in degrees is about 114.592 degrees.
Let us see how to convert 2 radians to degrees and also solve a few examples using this.
|1.||What is 2 Radians to Degrees?|
|2.||How to Convert 2 Radians in Degrees?|
|3.||FAQs on 2 Radians to Degrees|
What is 2 Radians to Degrees?
2 radians to degrees is approximately equivalent to 114.592 degrees in decimals and the value of 2 radians in degrees in terms of π is 360/π. We can convert an angle from one unit to the other unit using the following formulas:
We can understand these formulas using the following figure.
Let us see how to convert 2 radians to degrees using one of these formulas.
How to Convert 2 Radians in Degrees?
We can convert 2 radians in degrees using three methods. Here is the description of each of the methods:
We know that 1 radian to degrees is 57.296°. i.e.,
1 radian = 57.296°
Multiplying both sides by 2,
2(1 radian ) = 2(57.296°)
2 radian = 114.592°
Thus, 2 radians in degrees is 114.592°.
We can use the conversion formula of radians to degrees to convert 2 radians to degrees. The formula is:
Degrees = Radians × 180°/π
Substitute "Radians = 2" here,
Degrees = 2 × 180°/π ≈ 114.592°.
The final answer is calculated using a calculator and is rounded to 3 decimals.
Thus, 2 radians to degrees is approximately equal to 114.592°.
We know that if we rotate the radius of a circle to complete one revolution, the angle formed at its center is 360 degrees. We also know that this angle in radians is 2π radians. i.e.,
2π radians = 360°
Dividing both sides by π,
2 radians = 360°/π ≈ 114.592°.
We can understand this easily using the following figure.
Hence, 2 radians to degrees is equivalent to 360°/π (or) 114.592°.
Important Notes on 2 Radians in Degrees:
- 1 radian ≈ 57.296° and hence 2 radians ≈ 114.592°.
- An angle without any unit is in radians. For example, if you see the angle to be just 2 somewhere, it means that it is 2 radians.
- To express the angle which is in radians in degrees, we multiply it by 180°/π.
- To express the angle which is in degrees in radians, we multiply it by π/180°.
Examples on 2 Radians to Degrees
Example 1: Using the fact that 2 radians to degrees is 114.592 degrees, find the following angles in degrees: (a) 4 radians (b) 6 radians.
It is given that 2 radians = 114.592 degrees ... (1)
(a) Multiplying both sides of (1) by 2,
2(2 radians) = 2(114.592) degrees
4 radians = 229.184 degrees
(b) Multiplying both sides of (1) by 3,
3(2 radians) = 3(114.592) degrees
6 radians = 343.776 degrees
Answer: (a) 4 radians = 229.184° (b) 6 radians = 343.776°.
Example 2: Find the value of sin 2 by keeping the calculator in degrees mode. Round your answer to 2 decimals.
We know that in sin 2, angle 2 is in radians. We also know that 2 radians in degrees is 114.592°.
So sin 2 = sin 114.592° = 0.91.
The answer is calculated by using the "degrees" mode of the calculator.
Answer: sin 2 = 0.91.
Example 3: Given sin 114.592° = 0.91 and cos 114.592° = -0.42, Find the value of tan 2.
We know that 2 radians to degrees is 114.592°. i.e., 2 radians = 114.592°.
So tan 2 = tan 114.592°
= (sin 114.592°) / (cos 114.592°) (using the tangent formula)
= (0.91) / (-0.42)
Answer: tan 2 = -2.17.
FAQs on 2 Radians to Degrees
How to Convert 2 Radians to Degrees?
We have 360 degrees in radians is 2π. i.e., 2π = 360°. When we divide both sides by π, we get 2 radians = 360/π = 114.592 degrees.
What is the Value of 2 Radians to Degrees?
To convert 2 radians into degrees, we multiply the angle by 180°/π. Then we get 2 radians = 2 × 180°/π = 114.592°.
How is 2 Radians Equal to 114.592 Degrees?
We know that 1 radian = 57.296. By multiplying this equation on both sides by 2, we get 2 radians = 114.592°.
What is Degree Equivalent of 2 Radians?
An angle can be changed from radians to degrees and also from degrees to radians. The degree equivalent of 2 radians is 2 × 180/π which is approximately equal to 114.592.
What is 2 Radians in Degrees in Terms of Pi?
We know that 2π radian = 360°. To find the angle 2 radians in terms of π, just divide the equation both sides by π, then we get 2 radians = 360°/π.
What is 2 Radians to Degrees on a Circle?
In a circle, the angle at the center is 2π radians = 360 degrees. If we divide this by π, we get 2 radians = 360/π (or) equivalently 114.592.