What are actually these sin(sine), cos(cosine), tan(tangent), cosec, sec, cot, etc?

Question

I have found these things very confusing i doing maths questions. I would like to know what is the general meaning of these things, how it formed, how it works and all these things. And if possible, a name of a website from whare i can get these information, or a person, to whom I can contact to find the answres.

Answer 1

they are called trigonometric functions as functions of an angle; they are important when studying triangles and modeling periodic phenomena, among many other applications. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. Most modern definitions are more complex and it will confuse you further.

The easiest way to understand it is by looking at a the right triangle definition of each of them and relate it to each other.

1) The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

2) The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse

3)The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side

4)The cosecant csc(A) is the multiplicative inverse of sin(A), i.e. the ratio of the length of the hypotenuse to the length of the opposite side:

5) The secant sec(A) is the multiplicative inverse of cos(A), i.e. the ratio of the length of the hypotenuse to the length of the adjacent side

6) The cotangent cot(A) is the multiplicative inverse of tan(A), i.e. the ratio of the length of the adjacent side to the length of the opposite side

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Answer 2

Thanks to the AAS, SSA and SSS and so on theorems, we know that, in right triangles (we know one angle is 90º right?), we don't need a whole bunch more information to get all the rest.

In other words, all right triangles with a 60º angle in them are similar triangles.

So some genius thought it would be a good idea to take a right triangle with a hypoteneuse of 1, and fool around with the angle measures and find out what the other leg lengths would be.
Then, he decided to take these leg lengths and set them into ratios, and these ratios would be the same in all right triangles with a set angle measure (like 60º). We can use those ratios to make the calculations easily, rather than having to go back to the AAS and SSA and SSS theorems each time.

Those ratios are the sine, cosine, tangent, etc.

If you have one of the two smaller angles in a right triangle, then the sine is the ratio: (the side opposite the angle in question divided by the hypoteneuse). abbr. SOH

The cosine is the ratio: (the side adjacent to the angle in question divided by the hypoteneuse). abbr CAH

The tangent is the ratio (the side opposite divided by the side adjacent) abbr TOA

memorize all three by SOHCAHTOA

Answer 3

These are the functions used in trigonometry which involves a right angled triangle . These have the general formula with respect to the position of theta as
SIN THETA= OPPOSITE/HYPOTENUSE
COS THETA=ADJACENT/HYPOTENUSE
TAN THETA=OPPOSITE/ADJACENT
The opposite,adjacent and hypotenuse are the sides oppsite to the theta, adjacent to the theta and opposite to the 90 degree respectively. As you move to higher standards you would find it difficult as there would be more operations in trigonometry, so i would advise you to kindly be through with the basics. There are three more basic formulas as:
SIN ^2 THETA+ COS ^2 THETA=1
1 - SEC^2 THETA= TAN^2 THETA
1- COSEC^2 THETA=COT^2 THETA
As far as other sites I am unable to help u since I do not know your expectations, For any other information you can also visit www.wikipedia.com where i found it would be useful for u as u need the basics which are clearly explained with meanings and diagrams.

Answer 4

I would like to add to the above, that all they are is relationships between sides of a right triangle (and you can always create two of these by dropping a perpendicular to the base of any other kind of triangle.

If I remember correnctly, sine is the hypotenuse over the side opposite, etc. These functions are useful for figuring out the lenth (distance) and area, and they are used in engineering and architecture among other things.

Answer 5

sin(x), cos(x), tan(x), csc(x), sec(x), cot(x) are trigonometric functions, where x is an angle of a right triangle.

We will say H is the hypotenuse, O is the side opposite angle x and A is the side adjacent to angle x.

sin(x) = O/H
cos(x) = A/H
tan(x) = O/A = sin(x)/cos(x)
csc(x) = H/O = 1/sin(x)
sec(x) = H/A = 1/cos(x)
cot(x) = A/O = cos(x)/sin(x)

All trig functions can be expressed in terms of the sine (side opposite measured angle) and cosine (side adjacent to measured angle). The rate of change of the sine function is equal to the cosine, and the rate of change of the cosine is the negative sine.

sin(x+y) = sin(x)cos(y) + sin(y)cos(x)
cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

arcsin, arccos, arctan etc are inverse trigonometric functions, i.e., arcsin(sin(x)) = x.

Hope this helps.

Answer 6

Trigonometry is en essence the measure of triangles. So, the functions you are mentioning above were all of them conceived since antiquity as a mean to achieve the goal of measure triangles (mainly for agricultural purposes and astronomical purposes ).

All the people before me, exactly defined to you the relationships between the sides of a triangle (specifically right triangle) but the origin of those functions is basically what I told you.

Good luck!

Answer 7

sin, cos, tan, cot, csc, and sec are the trig functions used in determining the lengths of sides or the angles of triangles.

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