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What is the result of projecting a spherical surface onto a plane?
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Why is the sum of the angles of spherical triangles always larger than the sum of the angles of plane triangles?
Because, to allow for the curvature of the spherical surface, each angle must be slightly larger than its plane-surface equivalent.
What is the difference between plane trigonometry and spherical trigonometry?
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
What is the difference of plane and spherical triangles?
The main difference is that the plane triangle is on a flat surface while the spherical triangle is on the surface of a sphere. One consequence is that the angles of a plane triangle sum to 2*pi radians (180 degrees) while those on a sphere sum to more than 2*pi radians.
What are the two branches of Trigonometry?
The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.
What is the importance of trigonometry in navigation?
Navigation takes place on the surface of a sphere, and it involves angles and distances. Spherical trigonometry was developed from plane trigonometry so that navigators could find their away over the Earth's surface.
Is plane mirror a spherical mirror why?
No, a plane mirror is not a spherical mirror. A plane mirror has a flat reflective surface, while a spherical mirror has a curved reflective surface. The shape of the mirror affects the way light is reflected, with spherical mirrors causing light rays to converge or diverge depending on their curvature.
Why is the sum of the angles of spherical triangles always larger than the sum of the angles of plane triangles?
Because, to allow for the curvature of the spherical surface, each angle must be slightly larger than its plane-surface equivalent.
What is the difference between plane trigonometry and spherical trigonometry?
Trigonometry is the study of plane and spherical triangles. Plane trigonometry deals with 2 Dimensional triangles like the ones you would draw on a piece of paper. But, spherical trigonometry deals with circles and 3 Dimensional triangles. Plane trigonometry uses different numbers and equations than spherical trigonometry. There's plane trigonometry, where you work with triangles on a flat surface, then there's spherical trigonometry, where you work with triangles on a sphere.
What is the difference of plane and spherical triangles?
The main difference is that the plane triangle is on a flat surface while the spherical triangle is on the surface of a sphere. One consequence is that the angles of a plane triangle sum to 2*pi radians (180 degrees) while those on a sphere sum to more than 2*pi radians.
What is a spherical path?
A spherical path is a curve on the surface of a sphere, typically connecting two points on the sphere. It is analogous to a straight line in a two-dimensional plane. On a globe, the equator is an example of a spherical path.
Which show the true shape of a continent map or globe?
A globe provides a more accurate representation of the true shape of a continent compared to a flat map, as it preserves the spherical nature of the Earth. Maps distort the shapes of continents due to the challenge of projecting a 3D surface onto a 2D plane.
What is the difference between plane and spherical triangles?
The difference between plane and spherical triangles is that plane triangles are constructed on a plane, and spherical triangles are constructed on the surface of a sphere. Let's take one example and run with it. Picture an equilateral triangle drawn on a plane. It has sides of equal length (naturally), and its interior angles are each 60 degrees (of course), and they sum to 180 degrees (like any and every other triangle). Now, let's take a sphere and construct that equilateral triangle on its surface. Picture an "equator" on a sphere, and cut that ball in half through the middle. Set the top half on a flat surface and cut it into four equal pieces. Now if you "peel up" the surface of one of those quarters and inspect that triangle, it will have three sides of equal length, and will have three right angles. Not possible on a plane, but easy as pie on the surface of a sphere. Spherical trig is the "next step up" from plane trig.
What is the definition of plane trigonometry?
Plane trigonometry is trigonometry carried out in (on) a plane. This could be contrasted with spherical trigonometry, which is trigonometry carried out on the surface of a sphere. Certainly there are some other more complex forms of trig.
What is an explanation of difference types of wavefront?
There are primarily two types of wavefronts: spherical wavefronts and plane wavefronts. Spherical wavefronts originate from a point source and propagate radially outward in all directions, similar to ripples in water. Plane wavefronts are flat, parallel surfaces that move uniformly in the same direction, similar to waves on the surface of a calm lake.
What are the two branches of Trigonometry?
The two branches of trigonometry are plane trigonometry, which deals with figures lying wholly in a single plane, and spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.
is plane mirror is a spherical mirror why?
plane mirror is never a spherical mirror,spherical mirrors are made up by cutting the part of the sherical balls and then polishing them.while the plane mirror is just a sheet of polished glass
What are the differences between plane mirror and spherical mirror?
Plane mirrors have a flat reflective surface, while spherical mirrors have a curved reflective surface. Plane mirrors produce images that are virtual, upright and the same size as the object, whereas spherical mirrors can produce both real and virtual images that may be magnified or reduced in size. The focal point of a plane mirror is at infinity, whereas spherical mirrors have a specific focal point where light rays converge (concave mirror) or diverge (convex mirror).
