Math SAT 2 Trig Question

p(t)= 110+20sin(160(pi)t)

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?

pls help

bump up my post

But here goes.
Set = to 130
subtract 110 from both sides; now the left is 20.
Divide both sides by 20; now the equation is 1= sin (160(pi)t)

Sin = 1 at 90, 270
90= 160 pi t, solve for t ( sorry, I don’t have a calculator handy)
270= 160 pi t… ditto

@bjkmom thank you :slight_smile:

@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.

You’re right MITer.

Serves me right; I haven’t taught trig since 2000.

@MITer94 thank you. I was just quoting from my book. Thank you, that clarifies it :slight_smile:

No problem.

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.


I see.

Thank you for all of your help, I appreciate your help and you do a good thing in helping a lot of CC members.

Sat 2’s in the morning :slight_smile:

Good luck!

@MITer94 thanks mate :slight_smile:

Good luck in college too bro :slight_smile: