Trig identities, what does this mean?

[supernova1203]

Tan theta=sin theta/cos theta

What does that identity mean? What does it say about the triangle?

And what on Earth is an identity?

I understand everything taught in the course so far, trig ratios, reciprocal trig ratios, special angles etc etc...but i have no idea what identities mean, some of them i recognize because they are reciprocal trig functions like

sin theta=1/cosecant theta -->which means that sin theta the angle is reciprocal to its cosecant... but Tan theta=Sin theta/cos theta... what does that even mean?or what about cotangent theta = cos theta/sin theta

Im lost mostly in trig identities @_@

and please no dictionary definitions, pretend your trying to explain these concepts to your 80 year old grandma @_@

from what i can gather an identity is basically left side equals right side?

for some reason reciprocal trig identities are easier for me to comprehend...because i know what a reciprocal is

omg i just read a page where it shows the sides as being sin theta and cos theta...i thought theta was for angles then why did they mark the sides of the triangle like this?

 

[armolinasf]

for tan theta if you break up sin and cos into their parts, that is op/hy and adj/hp and divide you will get the definition of tan which is op/adj. cot is when you divide cos/sin again the hyp will cancel out.

Identities are like masks to an actor: the same actor can wear many masks. There synonyms telling you the same thing. so yes one side does equal another.

hope this helps a bit

 

[MacLaddy]

I would recommend going to
http://www.khanacademy.org/video/trigonometric-identities?playlist=Trigonometry
And watching this video, along with the following four. He does a good job on breaking it down in simpler terms.

 

[supernova1203]

I would recommend going to
http://www.khanacademy.org/video/trigonometric-identities?playlist=Trigonometry
And watching this video, along with the following four. He does a good job on breaking it down in simpler terms.

your right, i just checked it out, makes a whole lot more sense than how the teachers explain it...

 

[mharten1]

Sin(θ) is not an angle, or a side. Sine, Cosine, and Tangent are all functions of angles. In right triangle, these give the ratios of sides.

θ is an angle, however.

 

[armolinasf]

Are sine, cosine, and tan defined for anything other than a right triangle? and if not why not?

 

[lurflurf]

Yes; sine, cosine, and tangent are defined for all triangles. They can also be defined without reference to triangles. When working with triangles, oblique triangles are thought of as being two right triangles.

 

[mharten1]

Are sine, cosine, and tan defined for anything other than a right triangle? and if not why not?

They also apply to oblique triangles, although you have to use the law of sines and cosines.