Solving sin(t^2)-(t^2)=0


by wutang42
Tags: sint2t20, solving
wutang42
wutang42 is offline
#1
Dec7-12, 11:31 PM
P: 3
1. The problem statement, all variables and given/known data

Solve
sin(t2) - t2 =0. for t

2. Relevant equations

None, besides various trig identities. This was actually a dynamics problem where I had to solve for time, and this is simply the equation you get after summing up all the forces.

3. The attempt at a solution


Now obviously 0 is a solution, and when I plug it into wolfram alpha I get t=1.04, which I know is the correct answer because my professor told us that in class. However, when I plug it into my TI-89, the only solution that comes out is 0, and when I graph it, it doesn't show the 1.04 solution either.



So, my question is, is there any way to solve this problem without a numerical solver? And if not, is there any way to plug it into my TI 89 in order to get the correct answer?
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
Mentallic
Mentallic is offline
#2
Dec8-12, 12:09 AM
HW Helper
P: 3,436
Quote Quote by wutang42 View Post
1. The problem statement, all variables and given/known data

Solve
sin(t2) - t2 =0. for t

2. Relevant equations

None, besides various trig identities. This was actually a dynamics problem where I had to solve for time, and this is simply the equation you get after summing up all the forces.

3. The attempt at a solution


Now obviously 0 is a solution, and when I plug it into wolfram alpha I get t=1.04, which I know is the correct answer because my professor told us that in class. However, when I plug it into my TI-89, the only solution that comes out is 0, and when I graph it, it doesn't show the 1.04 solution either.



So, my question is, is there any way to solve this problem without a numerical solver? And if not, is there any way to plug it into my TI 89 in order to get the correct answer?
t=1.04 can't possibly be a solution because

[tex]\sin(t^2)-t^2 < 0[/tex]

for that value of t. How can you tell? Because the max sin can be is 1, and 1.042>1.
jedishrfu
jedishrfu is offline
#3
Dec8-12, 12:47 AM
P: 2,477
for small radian values sin(x) ≈ x hence
and that's probably the best you can do.

wutang42
wutang42 is offline
#4
Dec8-12, 12:12 PM
P: 3

Solving sin(t^2)-(t^2)=0


Shoot, I realized that I misstated the problem. It's actually 1.225*sin(t2) - t2 =0

But yeah, I realize that it still doesn't make much sense, but this is the answer and the graph that wolfram alpha spits out, and I'm just trying to figure out how to replicate that either on paper or on my calculator
Attached Thumbnails
Screen Shot 2012-12-08 at 10.10.34 AM.png  
LCKurtz
LCKurtz is offline
#5
Dec8-12, 01:56 PM
HW Helper
Thanks
PF Gold
LCKurtz's Avatar
P: 7,202
Quote Quote by wutang42 View Post
Shoot, I realized that I misstated the problem. It's actually 1.225*sin(t2) - t2 =0

But yeah, I realize that it still doesn't make much sense, but this is the answer and the graph that wolfram alpha spits out, and I'm just trying to figure out how to replicate that either on paper or on my calculator
Why doesn't it make much sense? Your graph clearly shows zeroes near ##\pm 1##. You could work it by hand with your calculator using Newton's method with a starting value of ##x=1##. Make sure your calculator is in radian mode.
wutang42
wutang42 is offline
#6
Dec8-12, 02:06 PM
P: 3
Quote Quote by LCKurtz View Post
Why doesn't it make much sense? Your graph clearly shows zeroes near ##\pm 1##. You could work it by hand with your calculator using Newton's method with a starting value of ##x=1##.Make sure your calculator is in radian mode.
Aaaaand there's my problem. I was doing it in degrees the whole time on my calculator, and couldn't figure out why my graph looked nothing like the wolfram graph. Derp. Thanks!!
Mentallic
Mentallic is offline
#7
Dec8-12, 03:27 PM
HW Helper
P: 3,436
Quote Quote by wutang42 View Post
Aaaaand there's my problem. I was doing it in degrees the whole time on my calculator, and couldn't figure out why my graph looked nothing like the wolfram graph. Derp. Thanks!!
Common mistake I've done it enough times myself that it's now on my checklist of things that could have gone wrong.


Register to reply

Related Discussions
Solving a DE Calculus & Beyond Homework 0
Help with solving PDE Differential Equations 3
Solving for X Introductory Physics Homework 5
solving int (sin(x)/x)^2 dx Calculus & Beyond Homework 7
solving for x General Math 12