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