Can \cos(\theta-\lambda) Be Used to Show Sin C in Addition Formula/Sine Rule?

[r_maths]

http://img117.imageshack.us/img117/1482/graph015tt6.png
I know an alternative way of showing Sin C is cos 'theta'.
Thanks

 

[Feldoh]

What is angle C? I can't make it out in the picture... Also could you show your attempt of the problems?

 

[r_maths]

Angle C is pi/2 - theta (radians) "pi over two minus theta" ie. 90 deegrees - theta.
I did show my attempt at it, i couldn't get further.

 

[HallsofIvy]

Certainly, since the angles in a triangle add to $2\pi$ radians, $B= 2\pi- \lambda- (\pi/2- \theta)= 3\pi/2- (\theta- \lambda)$.
Okay, using sin(a+ b)= sin(a)cos(b)- cos(a)sin(b)[/itex], what is
$sin(3\pi/2+ (-(\theta- \lambda)))$?

 

[cristo]

Certainly, since the angles in a triangle add to $2\pi$ radians,

The angles of a triangle add upto $\pi$ radians

$B= 2\pi- \lambda- (\pi/2- \theta)= 3\pi/2- (\theta- \lambda)$.

thus $B=\pi-\lambda-(\pi/2-\theta)=\pi/2+(\theta-\lambda)$

Okay, using sin(a+ b)= sin(a)cos(b)- cos(a)sin(b)[/itex], what is
$sin(3\pi/2+ (-(\theta- \lambda)))$?

The expression you require is therefore $\sin(\pi/2+(\theta-\lambda))$ = ?

 

[r_maths]

$\cos(\theta-\lambda)$

Thanks