what are sines and cosines?

Question

math

Answer 1

In mathematics, the trigonometric functions (sine, cosine, tangent, etc.) 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.

sine = (opposite)/(hypotenuse)
cosine = (adjacent)/(hypotenuse)
tangent = (opposite)/(adjacent)

Answer 2

Sines and cosines are two "trigonometric functions" of angles.

They are first introduced by considering a right-angled triangle. If you sketch such a triangle, and select one of the acute angles to focus on (say the angle at vertex ' A ' in a triangle ABC with the right-angle at ' C '), you'll notice that there is a hypoteneuse (the longest side), AB, which is often referred to as ' H ' (for 'hypoteneuse.' There's an "adjacent side," ' A ' or AC, and an "opposite side," ' O ' or BC.

These short letters ' O,' ' H,' and ' A ' are very useful mnemonics, helping one to remember what sines (sin), cosines (cos), and another function, tangents (tan) are:

sin (A) = O/H; cos (A) = A/H; tan (A) = O/A.

There is a mnemonic that all students meet when beginning to learn trigonometry:

SOHCAHTOA;

It lists the order that is shown above, meaning S (the sine) is O/H, etc.

Although these functions are initially introduced for acute angles, they also exist for any general value of the angle. They crop up, sometimes almost unexpectedly, in a great variety of physical problems in the world, characterizing things like the small ampitude motion (or "simple harmonic motion") of a pendulum, for example.

I hope this helps.

Live long and prosper.

Answer 3

Take a right triangle ABC. Let
Lets take for example when BC=2cm, AC=4cm. So, BC/AC=2/4=1/2. So the angle is 30(sin(30)=1/2).

There is some relations between sin(x) and cos(x). Some are...
1.sin(x)=cos(90-x) and cos(x)=sin(90-x)
Eg:sin30=1/2. So cos(90-30) or cos60 also equal to 1/2
2.sin^2(x)+cos^2(x)=1

Answer 4

In their simplest form, they are ratios of the sides of a triangle ABC which contains a right angle at C.
sin(A) = BC/AB and cos(A) = AC/AB.