Since a full circle has 360degrees and this circle only has two angles, subtract the arc of the known angle to find the arc of the unknown angle.
Angle DGF + angle DEF= 360degrees
Angle DGF + 70degrees= 360 degrees
Angle DGF = 290 degrees
The arc of the unknown angle is 290 degrees
Step-by-step explanation:
Consider an engineering material of initial length Lo, Area (A), Modulus of elasticity (E) and applied a force P due to which change in the length of the material is δ2 from it’s original length (Lo)
Initial length of the material is Lo. Hence, at time t = 0 when no force applied on the material the length of the material will not change (i.e., at time t=0, δ1 = 0)
Modulus of elasticity of the material:
![E=\frac{P \cdot L_{o}}{A\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BP%20%5Ccdot%20L_%7Bo%7D%7D%7BA%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
Area of the material:
![A=\frac{P \cdot L_{o}}{E\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7BP%20%5Ccdot%20L_%7Bo%7D%7D%7BE%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
Length of the material:
![E=\frac{P \cdot L_{0}}{A\left[\delta_{2}-\delta_{1}\right]}](https://tex.z-dn.net/?f=E%3D%5Cfrac%7BP%20%5Ccdot%20L_%7B0%7D%7D%7BA%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D)
![L_{0}=\frac{E \cdot A\left[\delta_{2}-\delta_{1}\right]}{P}](https://tex.z-dn.net/?f=L_%7B0%7D%3D%5Cfrac%7BE%20%5Ccdot%20A%5Cleft%5B%5Cdelta_%7B2%7D-%5Cdelta_%7B1%7D%5Cright%5D%7D%7BP%7D)
Solve for x:
2 sin^2(x) = 1
Divide both sides by 2:
sin^2(x) = 1/2
Take the square root of both sides:
sin(x) = 1/sqrt(2) or sin(x) = -1/sqrt(2)
Take the inverse sine of both sides:
x = 2 π n_1 + (3 π)/4 for n_1 element Z or x = 2 π n_2 + π/4 for n_2 element Z or sin(x) = -1/sqrt(2)
Take the inverse sine of both sides:
Answer: x = 2 π n_1 + (3 π)/4 for n_1 element Z or x = 2 π n_2 + π/4 for n_2 element Z or x = 2 π n_3 + (5 π)/4 for n_3 element Z or x = 2 π n_4 + (7 π)/4 for n_4 element Z
