(Geometry!)?

plz help me: (Geometry!)?
what are the sin , cos , and tan used for , please make some examples for each one.

Answers and Views:

Answer by dina *
sin, cos, tan are used to find the angles or length of a triangle.
lets say you have a 30-60-90 triangle with lengths of 2, 1, and radical 3.
sin [angle]= opposide side of the angle / hypontenuse.
cos [angle]= adjecant side of the angel / hypontenuse.
tan [angel]= opposide side of the angle / adjecant side of the angle
eg:
sin 30 = 1 / 2
cos 30 = radical 3 / 2
tan 30 = 1 / radical 3

Answer by garfyldrox
The sine function is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let be an angle measured counterclockwise from the x-axis along an arc of the unit circle. Then is the vertical coordinate of the arc endpoint. As a result of this definition, the sine function is periodic with period . By the Pythagorean theorem, also obeys the identity .

The cosine function is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let be an angle measured counterclockwise from the x-axis along the arc of the unit circle. Then is the horizontal coordinate of the arc endpoint. As a result of this definition, the cosine function is periodic with period . By the Pythagorean theorem, also obeys the identity

The tangent function is defined as where is the sine function and is the cosine function. The notation is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix).

The word “tangent” also has an important related meaning as a line or plane which touches a given curve or solid at a single point. These geometrical objects are then called a tangent line or tangent plane, respectively.

Answer by fcas80
If I had a tree on the edge of a river, and I hung a rope from the top of the tree and threw the rope just across the river so it landed on the shore, and I knew the length of the rope and the angle it made with the horizontal ground, then I could use trig functions to calculate either the height of the tree or the width of the river.

Answer by J & C
The sin, cos and tangent are used to find the side of a right triangle (one which has a 90 degree angle) given an angle of the triangle (besides the 90 degree one). To remember how to use them remember:
SOHCAHTOA

Let x be an angle then SOHCAHTOA can be easily remembered and used to find:
Sin x=Opposite/Hypotenuse
Cos x=Adjacent/Hypotenuse
Tan x=Opposite/Adjacent

Answer by IWasWondering
They can be used (practically) for taking measurements. They also crop up in periodic motion and lots of other areas of mathematics. They are functions of angles.

It is simplest to see from a right triangle ABC, where the angle B is the 90 degree angle. In this angle the length of the side AB might be called a, the length of the side BC might be called b and the length of the side CA might be called c. (draw it out.)

Side c is the hypotenuse.

For angle A, the Opposite side is b. For Angle A, the Adjacent side is a.

For Angle C, the opposite side is a, the Adjacent side is b.

Given this triangle,
the sin(A) = Opposite/Hypotenuse = b/c.
cos(A) = Adjacent/Hypotenuse = a/c.
tan(A) = sin(A)/cos(A) = b/a = Opposite/Adjacent.

If you’re measuring height of a building and know how far you are from the building (adjacent side) and the angle you must look up to see the top edge of the building, tou can use (adjacent*tan(angle looking up)) = height of building.

Answer by iMi
Many many things is the answer.

First, in a right triangle, we can find the length of a missing side or an angle by remembering soh cah toa. The sign of an angle is the ratio of the opposite leg of the triangle, over the hypotenuse (longest leg, opposite the 90 degree angle). Cosine is the adjacent over the hypotenuse. And tangent is the opposite over the adjacent.

Let’s say you have a problem that says “a right triangle has a hypotenuse of length 4cm and one angle at 35 degrees, find all angles and side lengths”. You can do this because of sin, cos, and tan.

you could figure out the 3rd angle since all triangles have angles that add up to 180 degrees. 180 – (90 + 35) = 55 (you could also find this with sin, cos, tan, solving for the angle with arcsin, arccos, or arctan). So you just need to find the two shorter sides… we can work with the 35degree angle for both…

soh
sin (35) = opposite / (4)
the side opposite to the 35 degree angle is about 2.3cm.

cah
cos (35) = adjacent / (4)
the side adjacent to the 35 degree angle is about 3.3cm.

This is a lot easier to understand with a drawing so I will add a link at the end.

When it comes to radians, which you might learn later if you are learning these for triangles at the moment, it relates to the unit circle. Here pi radians is equivilent to 180 degrees. This is also in the link because I think it’s almost impossible to explain without pictures.

Finally, when we graph these functions, sine and cosine describe periodic curves (if you have a graphing calculator you can see this by graphing : cos(X) or sin(X) (be sure to put your calculator in radians first under the mode option most likely). Sine and cosine both have a y max and min of 1 and -1 respectively. Sine crosses the y axis at (0,0) and continues to cross the x-axis at pi, 2pi, 3pi and so on. Cosine, crossing the y-axis at 1 crosses the x axis at pi/2, 3pi/2 and so on. These graphs are often used to decribe natural motions like waves, pulses, paths… et cetera because they are easily manipulated to look like other graphs.

Here is a good link about triangles and graphing applications

Here is a good link from wikipedia explaining their relation to the unit circle https://en.wikipedia.org/wiki/Unit_circle

Here is wikipedia’s in-depth (look at the pictures if nothing else) explanation of sine cosine and tangent https://en.wikipedia.org/wiki/Sine

Answer by questions
oh god, this was easy but it really depends all upon the measurments that are given to you. remember sohcahtoa
s=sin
c=cos
t=tan(tangent)

adjacent over opposit=sin
adjacent over hypotenuse=cos
opposite over adjacent=tan
(i am sorry if this is incorrect i havnt worked with this in quite some time i did my best at remembering)