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60 Degrees to Radians
Before going to convert 60 degrees to radians, let us recall a few facts about "degrees" and "radians". These are the units of measurements of an angle. i.e., an angle is measured in degrees or radians.
- 1 radian is equal to the angle subtended by an arc of a circle whose length is same as that of the radius of the circle.
- 1 degree is one part of the angle at the center of the circle when the angle (complete angle) is divided into 360 parts.
Let us see what is 60 degrees in radians and how to prove it in different methods. Let us solve a few examples and do some practice problems.
|1.||What is 60 Degrees to Radians?|
|2.||Converting 60 Degrees to Radians|
|3.||FAQs on 60 Degrees to Radians|
What is 60 Degrees to Radians?
- Angle in radians = Angle in degrees × π/180°
- Angle in degrees = Angle in radians × 180°/ π
Remember any angle in radians either has a π in it; or it neither has π nor has any symbol (like °) next to it. So to convert an angle from degrees to radians we multiply it by π/180° (rather than by 180°/π) as we should have π in the numerator of any angle in radians.
Converting 60 Degrees to Radians
We can convert 60 degrees to radians in multiple methods. Let us discuss each of these methods one by one.
We use the conversion formula to convert degrees into radians:
Angle in radians = Angle in degrees × π/180°
Here, our angle in degrees is 60°. Let us substitute this in the above formula:
Angle in radians = 60° × π/180° = π/3.
Thus, 60 degrees in radians is π/3.
We know that the angle at the center of a circle is 360 degrees. It is equivalent to 2π in radians. i.e.,
360° = 2π
Dividing both sides by 6 (as we want to find the value of 60 degrees in radians),
360°/6 = 2π/6
60° = π/3
Thus, the value of 60 degrees to radians is π/3.
Important Notes on 60 Degrees to Radians:
- 60 degrees is equivalent to π/3 in radians.
- Any angle can be converted from degrees to radians and vice versa.
- For converting an angle from degrees to radians, just multiply it by π/180°.
- For converting an angle from radians to degrees, just multiply it by 180°/π.
Examples Using 60 Degrees in Radians
Example 1: We know that 60 degrees in radians is π/3. Use this fact to convert the following angles into radians: (a) 30° (b) 120°.
It is given that 60° = π/3 ... (1)
(a) Dividing both sides of (1) by 2,
60°/2 = (π/3) / 2
30° = π/6
(b) Multiplying both sides of (1) by 2,
60° × 2 = (π/3) × 2
120° = 2π/3
Answer: (a) 30° = π/6 (b) 120° = 2π/3.
Example 2: Find the value of tan 60° using the following facts: sin π/3 = √3/2 and cos π/3 = 1/2.
We know that 60 degrees to radians is π/3.
So tan 60° = tan π/3
= (sin π/3)/(cos π/3) (using tangent formula)
Answer: tan 60° = √3.
Example 3: What is the value of 60° in decimals? Round your answer to 2 decimals and use π = 3.142.
We know that the value of 60 degrees in radians is π/3. i.e.,
60° = π/3
= 3.142 / 3
Answer: 60° ≈ 1.05
FAQs on 60 Degrees to Radians
How to Convert 60 Degrees to Radians?
The value of 60 degrees in radians is π/3. This is because 2π = 360 degrees. When we divide both sides by 6, we get π/3 = 60 degrees.
What is 60 Degrees to Radians in Terms of Pi?
To convert 60 degrees into radians, we just multiply it by π/180°. Then 60° = 60° × π/180° = π/3 radians.
How is 60 Degrees Equal to Pi/3?
60° is in degrees and π/3 is in radians. To convert 60 degrees in radians, we just use the conversion formula 180° = π. Dividing both sides by 3, we get 60° = π/3.
What is Radian Equivalent of 60 Degrees?
Any angle can be converted from radians to degrees and vice versa. The radian equivalent of 60 degrees is obtained by multiplying it by π/180°. Then we get π/3.
What is 180 Degrees in Pi if 60 Degrees in Radians is Pi/3?
It is given that 60 degrees in radians is π/3. i.e., 60 degrees = π/3. Multiplying both sides by 3, we get 3(60 degrees) = 3(π/3). This gives 180 degrees = π.
What is 60 Degrees to Radians on Unit Circle?
On unit circle, we have all angles labeled both in degrees and radians. On the unit circle, 60 degrees in radians is π/3.