6 x -1 = -6
-6 - (3) = -9
Not 100% sure if that's correct but I tried :)
Answer:
- A"(-1, -2)
- B"(6, 0)
- C"(3, 3)
- (x, y) ⇒ (x+1, y+1)
Step-by-step explanation:
Translation vectors add, and the addition is commutative and associative.
__
The first translation adds (-1, 2) to the original coordinates. The second translation adds (2, -1) to the original coordinates. The two translations together add ...
(-1, 2) +(2, -1) = (-1+2, 2-1) = (1, 1)
to the original coordinates.
The single rule representing this translation is ...
(x, y) ⇒ (x +1, y +1)
Then the doubly-translated coordinates are ...
A(-2, -3) ⇒ A"(-1, -2)
B(5, -1) ⇒ B"(6, 0)
C(2, 2) ⇒ C"(3, 3)
There are 4 possible heights and lengths. 1 and 136, 2 and 68, 4 and 34, 8 and 17 are the ones I came up with. Hope this helped.
It means that those 2 angles are the exact same length
Answer:
We have to prove
sin(α+β)-sin(α-β)=2 cos α sin β
We will take the left hand side to prove it equal to right hand side
So,
=sin(α+β)-sin(α-β) Eqn 1
We will use the following identities:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Putting the identities in eqn 1
=sin(α+β)-sin(α-β)
=[ sin α cos β+cos α sin β ]-[sin α cos β-cos α sin β ]
=sin α cos β+cos α sin β- sinα cos β+cos α sin β
sinα cosβ will be cancelled.
=cos α sin β+ cos α sin β
=2 cos α sin β
Hence,
sin(α+β)-sin(α-β)=2 cos α sin β
