Rewrite 2cos75° sin75° using a double angle identity

2cos75° sin75° = sin150°.

Step-by-step explanation:

Consider the provided information.

2cos75° sin75°

The double-Angle Identities  of sin(2x) is:

2 sin(x) cos(x) = sin(2x)

Replace x with 75° in the above formula.

2 sin(75°) cos(75°) = sin(2(75°))

2 sin(75°) cos(75°) = sin(150°)

2 cos(75°) sin(75°) = sin(150°)

Now compare the above equation and the provided expression. By comparison it can be concluded that the provided expression is equivalent to sin 150°

Hence, 2cos75° sin75° = sin150°.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart