Choosing to read the "dots" as multiplications, there are two real solutions:
But note that your formula is incorrect!!
cos2A is 2cos^2(A) - 1, not 1 - 2cos^2(A)
Note that 2*67.5 = 135, and that cos 135 = -cos 45, and that cos 45 = 1/sqrt(2)
So set A = 67.5 and use your formula (noting that cos 67.5 will be positive).
This graph should answer that question:
Oops! Careless of me. Thank you Guest.
With x = -3, then y = -2, so the distance between (5,2) and (-3,-2) is:
\(\sqrt{(-2-2)^2+(-3-5)^2}\rightarrow4\sqrt5\)
"Determine the shortest distance from the point H(5, 2) to the line through points J(-6, 4) and K(-2, -4)"
I get the following:
.
Assuming the skier is travelling in the positive x-direction and the 22.5° angle is measured from the x-axis, then:
Fx = 105*cos(22.5°) - 74.8 N ≈ 22.2 N
Fy = 105*sin(22.5°) N ≈ 40.2 N
"how do you simplify problems such as (1+sqrt(3)/3)/(1-sqrt(3)/3)"
Probabilistically:
Expected value = p*$300 - (1-p)*$1 where p = 0.001 is the probability of winning.
Hence Expected value = $0.3 - $0.999 → -$0.699 or -69.9 cents
+33665 
