Trigonometry

For Cartesian coordinates in n-dimensional space there are n axes which are [usually] orthogonal and which meet at a single point called the origin. The coordinates of any point in the n-space are defined by ordered n-tuples whose terms refer to the distances of the point, from the origin, along each of the axes.

x, y, and z ordinates from origin 0, x and y are two dimensional ordinates ie graph axis, z adds third dimension.

eg ordinates for point are say 10, 25, 15: start at 0, right for 10(x), left for 25(y), then vertically off the paper toward you for 15(z)

both turns are right angles

sin(90°) = 1

cos(90°) = 0

tan(90°) = ∞

sec(90°) = ∞

csc(90°) = 1

cot(90°) = 0

In trigonometry, when we look at right triangles, the cosine is the ratio of the length of the adjacent side to the length of the hypotenuse.

Trigonometry is the study of angles ond lengths. If you know one angle and one side length of a right traingle, you can find all the other values. If you know your distance from a tall object, and the angle made by the base of the tall object, your feet, and the top of the object, you can find the height of the object.

yes

The principal range of arc tan is an angle in the open interval (-pi/2, pi/2) radians = (-90, 90) degrees.

acute angle = less than 90o & greater than 0o right angle = 90o obtuse angle = greater than 90o & less than 180o straight angle = 180o reflex angle = greater than 180o

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1 million is 1,000,000

1 crore is 100 lakhs = 100,00,000 = 10,000,000

10 million is 1 crore

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.

A tetrahedron.

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a cube

comes from three Greek words; "tria"-three, "gonia"-angle, "metron"-measurement

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Like all prisms you find the area of one of the triangular faces and then multiply by the height.

Graphic designers use math because they have to measure out models to a certain scale. They need to know how to calculate exact measurements.

The parts of a cartesian coordinate system include the origin (point 0,0), the x-axis or abscissa, the y-axis or ordinate, and the quadrants into which the x and y axes divide the plane.

Pentehedron

In geometry, angles are studied mostly in relation to each other. In Trigonometry, angles are studied in relation to side lengths and triangles.

Trigonometric functions are periodic so they are many-to-one.

It is therefore important to define the domains and ranges of their inverses in such a way the the inverse function is not one-to-many. Thus the range for arcsin is [-pi/2, pi/2], arccos is [0, pi] and arctan is (-pi/2, pi/2).

However, these functions can be used, along with the periodicities to establish relations which extend solutions beyond the above ranges.

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If it is an elliptic oval, the circumference can be calculated by πab, where a and b are the lengths of the minor and major axes.

Triangular prism

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No. It is a triangular pyramid or a tetrahedron.

A triangular prism has 6 vertices and 5 faces.