The function f(x)=12sin(x−π4) is used to describe a water wave. The value x is the time in seconds, and f(x) is the position of the wave in feet above or below the normal water level. On which of these intervals does f−1(x) exist?

A
[0,π]

B
[3π4,7π4]

C
[π4,5π4]

D
[0,2π]

How many different three-digit numbers can be formed using the digits 1 comma 2 comma 9 comma 6 comma 4 comma 3 comma and 8 without repetition? for example, 664 is not allowed.

Two cars which are 40 miles apart start moving simultaneously in the same direction with constant speeds. if the speed of the car which is behind is 56 mph and the speed of the other car is 48 mph, how many hours will it take for the car which is behind to catch up the car ahead of it?

Prove sin2a + cos2a - 1 / sin2a + cos2a + 1 = 1 - tana / 1 + cota