Consider a triangle inscribed in the unit circle in the plane, with one vertex at (1, 0) and the two other vertices given by polar angles θ1 and θ2, in that order counterclockwise.
a) Express the area A of the triangle in terms of θ1 and θ2. What is the set of possible values for θ1 and θ2?
b) Find θ1 and θ2 that gives the maximum area.

Question

Consider a triangle inscribed in the  unit circle in the plane, with  one vertex at (1, 0)  and the  two  other  vertices  given  by  polar  angles  θ1 and  θ2,  in  that  order  counterclockwise. 
a)  Express  the  area  A  of  the  triangle  in  terms  of  θ1 and  θ2.  What  is  the  set  of  possible values  for  θ1 and  θ2? 
b)  Find  θ1 and  θ2 that gives the maximum area.

anonymous · Answer

All the math geniuses out there! Need help!

anonymous · Answer

but im not genius, man :D

anonymous · Answer

attachment

anonymous · Answer

Now, use herons formula

anonymous · Answer

Can u do that?

anonymous · Answer

Yeah, but i'm having trouble maximizing it.

anonymous · Answer

I got 

Sin theta1 - Sin theta2  +  Sin(theta2-theta1)

anonymous · Answer

yah estudier, i got that too. my problem is what is the range of  theta1 theta2, and what it the maximum area. i'm stuck in the 1st and 2nd derivative tests. really difficult in 2 variables.

anonymous · Answer

|dw:1350182086060:dw|$$A=\frac{ 1 }{ 2 }\sin(\theta _{2}-\theta _{1})+\frac{ 1 }{ 2 }\sin(\theta _{1})$$

anonymous · Answer

$$180-\theta _{1}=\theta _{2}$$