Cos(2θ) = 2cos^2θ - 1,
<span> cos^2(θ/2) </span>
<span>Solving </span>
<span>cos^2θ = [1 + cos(2θ)]/2. </span>
<span>replacing θ with θ/2 gives. </span>
<span>cos^2(θ/2) = (1 + cosθ)/2. </span>
<span>length of a polar curve of the form r = f(θ) on [a, b] is given by: </span>
<span>L = ∫ √[r^2 + (dr/dθ)^2] dθ (from θ=a to b).
hope this helps</span>
Answer: I think 131
Step-by-step explanation:
Answer:54 cm
Step-by-step explanation:
Given
Rods are joined to form a square
Perimeter of square is ![72\ cm](https://tex.z-dn.net/?f=72%5C%20cm)
Suppose a is the length of each rod so
Perimeter is ![4 a](https://tex.z-dn.net/?f=4%20a)
![\therefore 4a=72](https://tex.z-dn.net/?f=%5Ctherefore%204a%3D72)
![\Rightarrow a=\frac{72}{4}](https://tex.z-dn.net/?f=%5CRightarrow%20a%3D%5Cfrac%7B72%7D%7B4%7D)
![\Rightarrow a=18\ cm](https://tex.z-dn.net/?f=%5CRightarrow%20a%3D18%5C%20cm)
Now if rods are joined to form a square then
Perimeter is the sum of sides
Perimeter of (equilateral)triangle![=3a](https://tex.z-dn.net/?f=%3D3a)
![\Rightarrow =3\times 18](https://tex.z-dn.net/?f=%5CRightarrow%20%3D3%5Ctimes%2018)
![\Rightarrow =54\ cm](https://tex.z-dn.net/?f=%5CRightarrow%20%3D54%5C%20cm)