Using trigonometry and Fig. 2 in the ballistic pendulum write-up, show that the height h the pendulum rises after capturuing the ball is given by: h = R(1-cos(theta))

I thought that h = R(1-cos(theta)) was the same as h=Rsin(theta) which wouldn't make sense because h/R is not equal to sin(theta)... h is the vertical and theta is at the top...

Note that 1-cos\theta is NOT the same as sin \theta . If that was true then you would have 1 = sin \theta + cos\theta , but recall that actually:

1 = sin^2 \theta + cos^2 \theta