Gradians were most likely invented because right angles are 100 gradians which is easy to calculate and angles can be easily split in 2.
Circle Proportions:
1 = 400ᵍ
1/2 = 200ᵍ
1/4 = 100ᵍ
1/8 = 50ᵍ
1/16 = 25ᵍ….
If the 49.5 is in radians, then sin 49.5 ≈ −0.693 and so yes. If the 49.5 is in degrees, then sin 49.5o ≈ 0.760 If the 49.5 is in gradians, then sin 49.5 ≈ 0.702 If the 49.5 is in some other angle measurement, then you'll have to decide as I only know Degrees, Radians and Gradians angle measures. In Degrees, one full turn is 360o In Radians, one full turn is 2π radians ≈ 6.283 radians In Gradians, one full turn is 400 gradians. Radians are most useful in calculus. In fact you've used radians without realising it: The length of an arc of angle θ of a circle of radius r is θr when θ is measured in radians; the length of an arc of a circle round one full turn (ie the circumference of a circle) is θr = 2πr since one full turn is 2π in radians.
If the angles are measured in degrees or gradians, then: tan 3 > tan 2 > tan 1 If the angles are measured in radians, then: tan 1 > tan 3 > tan 2.
180 degrees = pi radians( 3.141592.... radians) . Hence 216/180 = x radians / pi radians. Algebraically rearrange x radians = 216 x pi / 180 x = 3.769911.... radians
60.00
It is pi - 2.47 = 0.67 radians (approx).
If the 49.5 is in radians, then sin 49.5 ≈ −0.693 and so yes. If the 49.5 is in degrees, then sin 49.5o ≈ 0.760 If the 49.5 is in gradians, then sin 49.5 ≈ 0.702 If the 49.5 is in some other angle measurement, then you'll have to decide as I only know Degrees, Radians and Gradians angle measures. In Degrees, one full turn is 360o In Radians, one full turn is 2π radians ≈ 6.283 radians In Gradians, one full turn is 400 gradians. Radians are most useful in calculus. In fact you've used radians without realising it: The length of an arc of angle θ of a circle of radius r is θr when θ is measured in radians; the length of an arc of a circle round one full turn (ie the circumference of a circle) is θr = 2πr since one full turn is 2π in radians.
120 what?degrees:120o = 120 x π ÷ 180 = 2π/3 radians≈ 2.094 radiansradians:120 radians = 120 radians gradians:120 gradians = 120 x π ÷ 200 = 3π/5 radians≈1.885 radiansOther angle measure:Divide 120 by the value of half a turn and multiply by π
arc tan -1.6 ≈ -57.99 + 180n degrees ≈ -1.01 + nπ radians ≈ -64.44 + 200n gradians.
Degrees are the usual measure when starting angles, but when calculus is done, radians are used.The US also had Gradians, but I've not noticed them used anywhere.A full turn is:360 degrees2π radians400 gradians
In degrees and in radians. There are also gradians, and several other units of measurement, not just two (as implied in the question).
If the angles are measured in degrees or gradians, then: tan 3 > tan 2 > tan 1 If the angles are measured in radians, then: tan 1 > tan 3 > tan 2.
The sine of an angle returns a dimensionless ratio, not an angle, which can be measured in either degrees or radians (or gradians, if you want to get technical). Sines and other trigonometric functions except angles as input to return this ratio. The sine of 50 degrees is .766044443119. The sine of 50 radians is -.262374853704.
iF the angle of 72 is measured in degrees, cos 72° ≈ 0.3090 If the angle of 72 is measured in radians, cos 72 rad ≈ −0.9673 If the angle of 72 is measured in gradians, cos 72 grad ≈ 0.4258
Grads or Gradians!
Yes, It is called Legends of the Guardians, and is said to be coming out in September.
180° = π radians → 45° = π × 45°/180° radians = π/4 radians
pi [radians] = 180 [degrees] 1 [degree] = pi/180 [radians] = 0.0174533 [radians] therefore, 2115 [degrees] = 2115 [degrees] * 0.0174533 [radians/degree] = 36.9 [radians]