The Mach number M of a supersonic airplane is the ratio of its speed to the speed of sound. When an airplane travels faster than the speed of sound, the sound waves form a cone behind the airplane. The Mach number is related to the apex angle θof the cone by sin(θ/ 2)=1 / M. (a) Use a half-angle formula to rewrite the equation in terms of cos θ. (b) Find the angle θthat corresponds to a Mach number of 1. (c) Find the angle θthat corresponds to a Mach number of 4.5. (d) The speed of sound is abou
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