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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.
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 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 the difference between plane waves and spherical waves?
spherical waves at far distance act like plane wave
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
Is plane mirror 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 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.
What happens when you slice a sphere with a plane?
The sphere forms a circle in the plane. There are two bits of sphere which are spherical caps with a circular base.
Difference of plane and spherical triangles?
A plane triangle looks like a common triangle. A plane triangle is solved with linear units. A spherical triangle is found inside of a sphere. This type of triangle is solved with angular units.
