Cool, but where is the diagram?
Answer:
-4 sqrt(7)/7
Step-by-step explanation:
csc theta = -4/3
csc theta = hypotenuse / opposite side
hypotenuse = 4
opposite = 3
Using the pythagorean theorem
a^2 + b^2 = c^2
3^2 + b^2 = 4^2
9+b^2 = 16
b^2 = 16-9
b^2 = 7
Taking the square root
sqrt(b^2) = sqrt(7)
b = sqrt(7)
We are in the third quadrant so only tan and cot are positive
that means the x and y values are "negative" so a = -3 and b = - sqrt(7)
sec theta = hypotenuse / adjacent
= 4/ - sqrt(7)
rationalizing
-4 sqrt(7)/ sqrt(7)* sqrt(7)
= -4 sqrt(7)/7
Change first equation
x - 2y = 1
add 2y to both side
x = 2y + 1
Plug into second equation
3(2y+1) - 6y = 3
Distributive property
6y + 3 - 6y = 3
y = 0, plug into first equation
x - 2(0) = 1, x = 1
Solution: x = 1, y = 0
The ratio fo boys to girls is 12:16
