Girard’s Formula for the area of a spherical triangle on the unit sphere is α +...
Girard’s Formula for the area of a spherical triangle on the unit sphere is α + β + γ − π .
Explain how antipodal points are used in the proof.
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Girard’s Formula for the area of a spherical triangle on the
unit sphere is α +...
Find the area of a spherical triangle with three right angles on a sphere with a...
Find the area of a spherical triangle with three right angles on a sphere with a radius of 2020 mi. Round to the nearest ten thousand square miles.
1. Let the angles of a triangle be α, β, and γ, with opposite sides of...
1. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides. (Round your answers to one decimal place.) α = 48°; β = 83°; c = 112 a= b= 2. Let the angles of a triangle be α, β, and γ, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides....
Solve the triangle (a is the side opposite α, b is opposite β, and c is...
Solve the triangle (a is the side opposite α, b is opposite β, and c is opposite γ ). You may estimate to the nearest hundredth but be sure to indicate it is only an estimate, not an exact answer. 1. β=30°, γ=45°, a=5. 2. γ=40°, a=1, b=2 3. a=6, b=2, c=5
4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from this the formula for the...
4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from this the formula for the area of a sphere of radius r.
4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from...
4. Suppose the same particle from Q3 is moving on a circular arc on the unit sphere, with θ = π/3, and beginning at 0 and ending at /4. Compute the line integral F. dr where the spherical form of the...
4. Suppose the same particle from Q3 is moving on a circular arc on the unit sphere, with θ = π/3, and beginning at 0 and ending at /4. Compute the line integral F. dr where the spherical form of the infinitesimal displacement vector, dr-dre, + rd0eθ + r sin(θ) dφ èošhould be used. Here, the spherical vector field is in effect.
4. Suppose the same particle from Q3 is moving on a circular arc on the unit sphere, with...
If Heron's formula is used to find the area of a triangle ABC having a :...
If Heron's formula is used to find the area of a triangle ABC having a : 3, B=5 and (:6
10. Use Heron's formula to calculate the area of a triangle. In below formula, a, b,...
10. Use Heron's formula to calculate the area of a triangle. In below formula, a, b, and c are the length of 3 sides of a triangle: s (a+b+c]/2 A Vs(s-a) (s-b) (s- e) Write a program to calculate area of triangle. Input a, b, e from console and display area.
Do not use I=delta/S!!! Use law of cosines Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, wha...
Do not use I=delta/S!!! Use law of cosines
Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r? Note in spherical geometry the angles sum is>180 Using below picture (this is what we are given), we should know angle b and the angle at the perpendicular. If we find the length on...
inal point β. Show plex constan I. Let γ be a directed smooth curve with initial point α and term directly from Definition 3 that f c dz-c(β-α), where c is any contioninge® Does the same formula hol...
inal point β. Show plex constan I. Let γ be a directed smooth curve with initial point α and term directly from Definition 3 that f c dz-c(β-α), where c is any contioninge® Does the same formula hold for integration along an arbitrary con β? Definition 3. Let f be a complex-valued function defined on the ined on the directed smooth curve y. We say that f is integrable along y if there complex number L that is the limit...
2. (a) State, without proof, the compound angle formulae for sin(a + β) and sin(α-β). 2 marks (b)...
2. (a) State, without proof, the compound angle formulae for sin(a + β) and sin(α-β). 2 marks (b) Let θ be a fixed real number with 0 < θ < π. Show that, for all real x, sin(z+θ)- sin(z-Asin(z + φ) where φ (π + θ)/2 and A-2 sin(θ/2) (Hint: use part (a) above). 10 marks] (c) Determine φ if A = V2 and if A = V3. [9 marks] The physical interpretation of the result in part (b) above...
4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from this the formula for the area of a sphere of radius r.
4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from...
4. Suppose the same particle from Q3 is moving on a circular arc on the unit sphere, with θ = π/3, and beginning at 0 and ending at /4. Compute the line integral F. dr where the spherical form of the infinitesimal displacement vector, dr-dre, + rd0eθ + r sin(θ) dφ èošhould be used. Here, the spherical vector field is in effect.
4. Suppose the same particle from Q3 is moving on a circular arc on the unit sphere, with...
If Heron's formula is used to find the area of a triangle ABC having a : 3, B=5 and (:6
10. Use Heron's formula to calculate the area of a triangle. In below formula, a, b, and c are the length of 3 sides of a triangle: s (a+b+c]/2 A Vs(s-a) (s-b) (s- e) Write a program to calculate area of triangle. Input a, b, e from console and display area.
Do not use I=delta/S!!! Use law of cosines
Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r? Note in spherical geometry the angles sum is>180 Using below picture (this is what we are given), we should know angle b and the angle at the perpendicular. If we find the length on...
inal point β. Show plex constan I. Let γ be a directed smooth curve with initial point α and term directly from Definition 3 that f c dz-c(β-α), where c is any contioninge® Does the same formula hold for integration along an arbitrary con β? Definition 3. Let f be a complex-valued function defined on the ined on the directed smooth curve y. We say that f is integrable along y if there complex number L that is the limit...
2. (a) State, without proof, the compound angle formulae for sin(a + β) and sin(α-β). 2 marks (b) Let θ be a fixed real number with 0 < θ < π. Show that, for all real x, sin(z+θ)- sin(z-Asin(z + φ) where φ (π + θ)/2 and A-2 sin(θ/2) (Hint: use part (a) above). 10 marks] (c) Determine φ if A = V2 and if A = V3. [9 marks] The physical interpretation of the result in part (b) above...
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