someone explain sine cosine tangent in trigonometry?

Question

http://www.gcse.com/maths/cos.htm
look on that page, why does 60 degrees equal 0.5 is 0.5 the length or what? arent they names of angles? how come you can find the length of an angle...confused..

Answer 1

soh cah toa

means Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent

to use this you need a right triangle
opposite means the length of the side opposite the angle you took the sin of
and hypotenuse is the length of height of the triangle that's the side that has a right angle at one end, that isn't either the 'opposite' or the 'adjacent'

you should draw it for your next problem

.5 is the ratio of the sides adjacent/hypotenuse
so let's say you have an angle of 60 degrees,
and somewhere along one of the lines coming from that angle is a perpendicular line(where the perpendicular line intersects our first line makes our hypotenuse value on the first line).
this new perpendicular line will also intersect the other line from the 60 degree angle (this is our adjacent value, it's adjacent our 60 degree angle).

wherever that line is(how ever long the hypotenuse),
the ratio of the length of the Adjacent / the length of the Hypoteneuse will = Cosine 60

dig it?

Answer 2

The trigonometry functions are ratios of sides of right-angled triangles.

To get the sine of an angle, you divide the length of the opposite site by the length of the hypotenuse. To get the cosine of the angle, you divide the adjacent side by the hypotenuse. And to get the tangent, you divide the opposite side by the adjacent side.

If you have a right-angled triangle where one of the other angles is 60 degrees, then the other angle must be 30 degrees (since all three must add up to 180). A 30-60-90 triangle will always have the shorter side being exactly half the length of the hypotenuse.

So when you look at the cosine of the 60 degree angle, it's the adjacent side divided by the hypotenuse, which will always be 1/2 which is 0.5.

Answer 3

hello i will try to help u.
we always work in a triangle rectangle.
first sin=opposit side/hypothenus
then cos= adjacent side/hypothenus
u just have to study this table:

n 0 1 2 3 4
ang 0 30 45 60 90
sin 0 1/2 √2/2 √3/2 1 √n/2
cos 1 √3/2 √2/2 1/2 0 1/sin
tg 0 1/√3 1 √3 - sin/cos
cotg - √3 1 1/√3 0 1/tg

Answer 4

Sines and cosines are reciprocals. One begits the other. If you do not understand this stuff so far you are in too far over your head. Better to back out and go to the begining and find out what it is that you missed.