What are sines, cosines, and tangents?

Question

I see a lot of trig questions on here. Mostly, they have sine, cosine, and tangent. What are they?

And what do people mean by sin 33.3 or something like that?

P.S. I'm a seventh grade geometry freak.

Answer 1

ratios of a right triangle.
Sine=opposite/hypotenuse
Cosine=adjacent/hypotenuse
Tan=opposite/adjacent

u can remeber it by soh cah toa

Answer 2

Everybody's answers are correct, but I'm guessing you're thinking, "What is the opposite? What is the adjacent?"

Since you're a geometry freak, you've already got a leg up on all this.

Take a 30-60-90 triangle.

You know the relationship between the short side, the long side, and the hypotenuse right? The hypotenuse is twice the length of the shorter side (the side next to the 60 degree angle), and the longer side is √3 times the shorter side.

So if the hypotenuse is 4, the shorter side is 2, and the height is 2√3, right?

Now, take a look at the 60 degree angle. The side that is opposite it is the longer side, and it's called the opposite. The shorter side is "adjacent" to the angle, so it's called the adjacent. And the hypotenuse is just called the hypotenuse.

The basic trig functions are just ratios of the sides.

sin 60 = opposite over hypotenuse = 2√3/4 = √3/2
cos 60 = adjacent over hypotenuse = 2/4 = 1/2
tan 60 = opposite over adjacent = 2√3/2 = √3

This is useful because, no matter how long the sides are, the angles always have the same ratios.

So, for instance, say that you knew that you had a right triangle, and that one angle was 55 degrees, and the side opposite it was 10 meters.

Then since, sin = opposite over hypotenuse, hypotenuse = opposite over sin, and the length of the hypotenuse would be 10/sin55 = 12.2 meters.

I dunno, maybe that wasn't necessary, but I thought I'd explain in more detail.

Answer 3

Wow, I'm impressed. Even when I had to, I didn't WANT to learn trig.

The sine of an angle measures how far up it points, and the cosine measures how far outward. It's easier to explain with an example.
If you have a ramp that goes up at an angle, the sine of that angle is how many inches, feet, or whatever it rises for each inch, foot, etc. of ramp. The cosine is how many units over it goes for each unit of ramp.

So for instance, say you had a ramp that went up at an angle of 30 degrees. The sine of 30 degrees is 1/2, so for every foot of ramp, it rises 6 inches. The cosine of 30 degrees is sqrt(3)/2, so for every foot of ramp, it extends outward 6*sqrt(3) inches.

The tangent is the sine divided by the cosine, and is a sort of measure of how steep the angle is. For instance, if the tangent is 1, then the sine and cosine are equal, so for each foot the ramp rises, it also extends one foot. If the tangent is 2, then the sine is twice the cosine, so for each foot the ramp rises, it only extends 6 inches. That means it's twice as steep as the ramp with a tangent of 1.

When someone writes sin 33.3, they are referring to the sine of 33.3 degrees. They really should write "degrees" after it, because there is another unit used to measure angles, radians. However, a full circle is only 2*pi radians, so if you see a number larger than that used to describe an angle, it's almost certainly degrees.

For the most part, you have to use a calculator to find sines and cosines, but there are a few that you'll be expected to memorize in trig class. The angles are 0, 30, 45, 60 and 90 degrees. The sines of those angles are 0, 1/2, sqrt(2)/2, sqrt(3)/2, and 1. The cosines are just the opposite: 1, sqrt(3)/2, sqrt(2)/2, 1/2, and 0. It helps to remember them if you notice the pattern: each one is sqrt(n)/2, and n ranges from 0 to 4.

If an angle points to the left instead of right, the cosine is negative. For instance, the angle 135 degrees is just as steep as the angle 45 degrees, but since it points left and not right, the cosine is -sqrt(2)/2.

If an angle points down instead of up, the sine is negative. For instance, the sine of 315 degrees is -sqrt(2)/2.

I'm sorry if I gave too much information, but I wasn't sure how much you wanted to know. I hope you stay interested in math. I never liked it much myself, but I love chemistry, so I know what it's like to enjoy a class most people hate.

Answer 4

they are concerned trigonometry of a right angled triangle usually. If ur a geometry freak then im sure u know what a hypotenuse is in a right angled triangle; the side opposite to the right angle. When we are concerned with sin, cos and tan, we choose one of the two angles in the triangle other than the right angle. The side opposite to this angle is called the opposite and the side next to this angle is called the adjacent and of course the third is the hypotenuse.

So presuming the angle we chose has a value of 33.3 degrees, then sin 33.3 is the ratio of the length of the opposite side to the length of the hypotenuse.

If we say tan 33.3 then that is the ratio of the length of the opposite side to the length of the adjacent side.

And finally if we say cos33.3 then that would be the ratio of the length of the adjacent side to the length of the hypotenuse side.

This is usually very helpful when we have a right angled triangle, with one known angle and one known side and we want to find the length of another side, or if we have two sides and we want to find a certain angle.

Answer 5

To answer the last part of your question, if people say "sin33.3", they mean the sine of the angle that is 33.3 degrees.
As the other two responders said, sine is "opposite over hypotenuse" in a right triangle, so if a triangle has one right angle, and one angle of 33.3 degrees, then the sine of the 33 degree angle is the length of the side NOT touching the 33.3 degree angle, divided by the long side of the triangle.

Answer 6

just remember SOH CAH TOA it is an anagram to explain each term.

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

these terms can only be used with a right triangle. when it says sin 33.3 it as talking about an angle measure. it is asking the sine of an angle with the measure of 33.3 degrees. if you draw a picture of the triangle you are working with you can line up which sides correspond with the angle you are using.

ex. sin 33.3 l \
l \
al \ c
l_ \
l_l_( _\33.3 degrees
b
so sin33.3= a/c

Answer 7

These are the ratios of a right triangle.
Sine=opposite/hypotenuse
Cosine=adjacent/hypotenuse
Tan=opposite/adjacent
There is also the sine law and cosine law:
a/SinA=b/SinB=c/SinC
and
a^2=b^2+c^2-2bcCosA
respectively, and tons of other trigonometric proofs and identities.
Do a wikipedia search if you want to learn more.

Answer 8

these are the ratios of the sides of a right triangle
sin=opp/hyp
cos=adj/hyp
and tan=opp/adj

Answer 9

They are the logistics found within log rythims