Sin^2theta=8(cos(-theta)-1). solve the equation on the interval 0

For the equation we can simplify inside the parenthesis first. Since cos(-theta) = cos(theta), we can rewrite as . We can distribute the 8 into the parenthesis to get . The idea is to solve for the angle theta. So we have to use the fact that sin^2 theta is the same as cos^2theta - 1. Trig identity. .

Put everything on one side of the equals sign and set the equation equal to 0. . We will factor this to solve for theta. It will be easier if we make a u substitution. Let u = cos theta; therefore, u^2 = cos^2 theta. Like this: . That factors very easily to u = 7 and u = 1. Replacing the u with cos theta: and . Since cosine only exists between 1 and -1, there is no solution for so the only solution is found in . There is only one place where cos theta = 1 and that is when theta is 0. So it doesn't really matter what the interval is!

i think it would be 42cm