Can someone explain to me about Cos, Sin, and Tan?

Question

Okay I am not stupid or anything I just have forgotten a lot about math. My last math class was my freshmen year in college. Now I am a Junior and I am taking physics and Cos, Sin, & Tan are what I am dealing with. It's embarrassing but i know high school kids know this too. Can anyone explain and give me an example of Cos, Sin, & Tan? I know the Pythagorean theorem already so you don't have to explain that.

Thanks!

Answer 1

Cos, Sin, and Tan are all ratios. So, you know about Pythagorean theroem, that's fine. You know that it only applies to triangles that have a right angle (90°). So, pick any of the other angles.

For that angle:

There are going to be two sides of the triangle attached to it. One will be the hypothenuse, the longest side of the triangle. The other will be called the adjacent leg. Therefore, the side that is not part of the angle will be the opposite leg.

Sin is equal to the ratio of the opposite leg divided by the hypothenuse

Cos is the ratio of the adjacent leg divided by the hypothenuse

Tan is the ratio of the opposite leg divided by the adjacent leg

This ratios will always hold for angles in right triangles that have the same measure.

Example:

Think about a right triangle whose legs measure 1 and (sqrt)3. Therefore, by the pythagorean theorem, the hypothenuse will be 2. Let's pick the angle that is formed with the hypothenuse and the leg that measures 1. This angle will measure 60° (pi/3 radians) Then:

Sin 60° = Sin (pi/3) = opp/hyp = (sqrt)3/2.

Cos 60° = Cos (pi/3) = adj/hyp = 1/2.

Tan 60° = Tan (pi/3) = opp/adj = (sqrt)3/1.

Hope it works.

Answer 2

SOHCAHTOA

sin=opposite/hypotenuse

cos=adjacent/hypotenuse

tan=opposite/adjacent

Answer 3

In a right triangle'

Sin = opposite leg / hypothenuse

Cos = adjacent leg / hypothenuse

Tan = opposite leg / adjacent leg

I don't have to give example 'cause i believe this is self explanatory and I assume you know what is opposite and adjacent leg in a Pythagorean theorem. ( / is divided by)

Answer 4

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

Answer 5

Remember: sin^2(x)+cos^2(x)=1

All based on Pythagorean Theorem of right triangles and the other angles beside the 90 degree one.....

Tan = sin/cos

Remember: SOH-CAH-TOA given a right triangle sin=opp/hyp, cos=adj/hyp, and tan=opp/adj

etc, etc

Google trig functions

Answer 6

http://en.wikipedia.org/wiki/Trigonometr...   has everything you need to know.

and

http://en.wikipedia.org/wiki/Trigonometr...   has everything you probably will ever need to know about Trigonometric identities

Answer 7

From what I can remember:

Cosine, sine and tangent of an angle are ratios of lengths of the sides

Sine of an angle = ratio of length of opposite / hypotenuse

cosine of an angle = ratio of length of adjacent / hypotenuse

tangent of an angle = ratio of opposite / adjacent

Answer 8

To understand cos, sin and tan is the easiest with the circle: the center is in (0,0), the radius is 1 and cos is horizontal ax and the sin is the other ax... so you "draw" the angle, (from the 0,0) and the point where the line cross the circle is (cos,sin) of that angle...

I hope you understand this. My english is not good enough to explain it better...

So tan=sin/cos

and you have to know a few basic eq:

sin^2+cos^2=1

sin(2x)=2sinxcosx

cos(2x)=cos^2(x)-sin^2(x)

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

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

and you need to know cos and sin from a few angle

sin 0=0

sin (pi/6)=1/2 (sin 30°)

sin (pi/4)=sqrt(2)/2 (sin 45°)

sin (pi/3)=sqrt(3)/2 (sin 60°)

sin (pi/2)=1 (sin 90°)

cos 0=1

cos (pi/6)=sqrt(3)/2 (cos 30°)

cos (pi/4)=sqrt(2)/2 (cos 45°)

cos (pi/3)=1/2 (cos 60°)

cos (pi/2)=0 (cos 90°)

I hope I was at least helpful... good luck!