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Questions about the radian system of mathematics in Senior High School Why is 1 radian equal to 180 ° / π, and why is 1 ° equal to (π / 180) rad?
A circle is 360 degrees, that is, 2 π radians. According to this ratio, each radian is 360 / 2 π = 180 / π degrees
One degree is 2 π / 360 = π / 180 radians
Definition of radian: the central angle of an arc whose arc length is equal to the radius of a circle is 1 radian, and radian has no unit? Why can we get this from this sentence (i.e. radian = arc length / radius = L / R) and why 1rad = (180 / π)?
The radian of a circle is 2 π, the circumference of a circle is 2 π R, the angle of a circle is 360, and the corresponding 1rad = (180 / π). If the radian of a sector is a, the arc length of the sector is a * r / 2 π, and the radian plays an important role in trigonometric functions. It doesn't matter if you don't understand it now. Wait until you use it in practice
1. Use radians to represent the set of angles of the final edge on the y-axis 2. What are cos0.75 ° and cos0.75 ° respectively and what is the difference?
3.141592653.=180°
cos0.75=cos（0.75π/180）°
If the circumference of the sector is 16cm and the center angle is 2 radians, the area of the sector is __
Let the radius of the sector be r, the area be s, and the center angle be α， be α= 2. The arc length is α r，
Then perimeter 16 = 2R+ α r=2r+2r=4r，∴r=4，
The area of the sector is: S = 1
two α r2=1
two × two × 16 = 16 (cm2), so the answer is 16 cm2．
It is known that the area of the sector is s. when the arc of the center angle of the sector is what, the perimeter of the sector is the smallest? And find the minimum value
Let the radius of the sector be r, the arc length be l, and the radian of the center angle of the sector be θ，
∴l=r θ， ∴S=1
2lr=1
2r2 θ， r=2S
l，
Circumference of sector C = L + 2R = L + 4S
l≥2
l•4S
l=4
S. If and only if l = 4S
When l, take the equal sign, and then l = 2
S，
And L = R θ，θ＝ l
r＝l2
2S＝2．
When the arc of the center angle of the sector is 2, the minimum circumference of the sector is 4
S．
Calculation formula of sector arc length It's best to simplify it step by step in three steps
Circumference = 2 × π × r
Arc length of sector: circumference = angle of sector: 360 °
So the arc length of the sector = 2 π R × Angle ÷ 360
I hope I can help you~~
If satisfied, please adopt a drop-down ~ ~ thank you~~~
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