Trig Identities via COW

[losfomot]

Howdy.

 

I've been working through this site called Calculus On the Web or COW.

 

It's been a great site so far, but I have a question on the section entitled 'Trigonometric Identities'

 

At the top of the page it shows the situation where

x = cos a

y = sin a

 

Then at the bottom of the same page, in an example, it says that

side B = tan a

 

I don't understand this. In the example at the top, isn't

 

side B = y coordinate = sin a

 

how can side B = tan a?

 

Unfortunately there is not a direct link to the page I'm talking about.

 

You must go here : Calculus On the Web

 

and then click on :

 

Precalculus Book

Functions

Trigonometry

Trig Identities

 

Then click on 'HELP' at the bottom and the page I am discussing will come up.

 

Thanks for any help

[Dave]

I think they're considering the case where the triangle is defined to have B of length tan(a), for one reason or another.

 

At least, that's my interpretation of it.

[losfomot]

I think they're considering the case where the triangle is defined to have B of length tan(a)' date=' for one reason or another.

 

At least, that's my interpretation of it.[/quote']

 

Yes, that makes some sense.

 

So the situation where the y coordinate = sin (a)

 

is only true if the circle has a radius of 1?

[Dave]

Indeed.

[losfomot]

Thanks Dave, One more question...

 

They give an identity for sin(2x) but not for sin(3x)

 

One of their later questions is:

 

put sin(3r) in terms of sin®

 

How would I figure this one out?

[Dave]

In much a similar way to sin(2x). You can use the fact that sin(3x) = sin(x + 2x), coupled with the formula for sin(2x) and the composite angle identity.

[losfomot]

In much a similar way to sin(2x). You can use the fact that sin(3x) = sin(x + 2x), coupled with the formula for sin(2x) and the composite angle identity.

 

 

Excellent, I got the question right.

 

Thanks again Dave.

[Dave]

No problem

 

It might interest you to know that there's a general formula for sin(nx), where n = 2, 3, ... You can find it here. The derivation isn't particularly hard, but you have to know a bit about complex numbers.