How does cos pi = -1 ?
Define cos(θ) as the x-coordinate of the point on the unit circle at an angle of θ in the counterclockwise direction from the positive x-axis. We know that π is halfway around a circle so the point on the unit circle will be the one opposite (1,0): i.e. it will be (−1,0). So cos(π)=−1. This also tells us that sin(π)=0, BTW.