a certain person’s blood pressure p(t), in millimeters of mercury, is modeled above as a function of time, t, in minutes. According to the model, how many times in the interval
0 less than or = to t less than or = to 1 does the person’s blood pressure reach a maximum of 130?

@fnaticMSiNate bjkmom’s solution appears flawed. The argument is in radians (if it were degrees it should say so), but also note that sin x = 1 iff x = π/2 + 2πk where k is an integer.

We want sin(160πt) = 1, so 160πt = π/2 + 2πk <–> 160t = 1/2 + 2k where k is an integer.

If k = -1, 1/2 + 2k = -1/2 which is too small. So k = 0 is the smallest integer value for k. It follows that we have k can be any integer in the set {0,1,2,…,79} (if k = 80, we have 160t = 160.5 but k > 1 in this case). There are 80 integers in {0,1,2,…,79} so the answer is 80.

Just to clarify, the argument of a trig function should always be in radians (unless the problem specifies otherwise). This is mostly because all of the trig identities, including ones encountered in calculus, work out nicely that way.