# TrigonometryWhy am I getting different answers for solving a trig equation graphically and algebraically

#### estex198

##### New member
Problem: Solve for t, 20 = 100 sin 2pi(50)t
note: pi = "pie"

I must be doing something wrong here. To solve algebraically, I first divide both sides by 100. Then, I get the inverse cosine of both sides, and set the angle in radians (.2013579208) equal to "2pi(50)t". Lastly I divide the derived angle by 100pi , which gives me .0063258456 for t.

When solving the equation graphically using a calculator, I get a different result for t. To solve graphically on my TI-83 Plus, I hit "y=" and enter for Y1 = 100*sin(2pi*50*X) - 20 and hit "graph". Once the graph has loaded I hit "2nd" + "calc" and choose the calculate zero function. I choose the intersection closest to x=0 to ensure the smallest positive angle, and for y=0, I get X = 6.4094E-4. This equates to 6.4094 * 10^-4, or .00064094, right? So why am I not getting the same answer for both of my solution methods?

#### Ackbach

##### Indicium Physicus
Staff member
Welcome to MHB, estex198!!

Problem: Solve for t, 20 = 100 sin 2pi(50)t
note: pi = "pie"

I must be doing something wrong here. To solve algebraically, I first divide both sides by 100. Then, I get the inverse cosine of both sides,
Why inverse cosine? The cosine function is not the function you need to invert here. Also, have you checked whether your calculator is in radians or degrees? That will be important.

#### SuperSonic4

##### Well-known member
MHB Math Helper
Problem: Solve for t, 20 = 100 sin 2pi(50)t
note: pi = "pie"

I must be doing something wrong here. To solve algebraically, I first divide both sides by 100. Then, I get the inverse cosine of both sides, and set the angle in radians (.2013579208) equal to "2pi(50)t". Lastly I divide the derived angle by 100pi , which gives me .0063258456 for t.

When solving the equation graphically using a calculator, I get a different result for t. To solve graphically on my TI-83 Plus, I hit "y=" and enter for Y1 = 100*sin(2pi*50*X) - 20 and hit "graph". Once the graph has loaded I hit "2nd" + "calc" and choose the calculate zero function. I choose the intersection closest to x=0 to ensure the smallest positive angle, and for y=0, I get X = 6.4094E-4. This equates to 6.4094 * 10^-4, or .00064094, right? So why am I not getting the same answer for both of my solution methods?

Why would you take inverse cosine if you have sine in the question?

#### estex198

##### New member
Forgive me for the typo. I mean inverse sine function. And yes, I've checked and rechecked that my calculator is in radian mode.

#### Ackbach

##### Indicium Physicus
Staff member
Forgive me for the typo. I mean inverse sine function. And yes, I've checked and rechecked that my calculator is in radian mode.
It's probably a calculator error. I'm getting what you're getting with your graphical approach. You should be evaluating:
$$t= \frac{ \arcsin(1/5)}{100 \pi},$$
right? On my calc (an HP 50g), I get $6.409 \times 10^{-4}$.

#### SuperSonic4

##### Well-known member
MHB Math Helper
Forgive me for the typo. I mean inverse sine function. And yes, I've checked and rechecked that my calculator is in radian mode.
I suspect (like Ackbach) it's a calculator error. Doing $$\displaystyle t = \dfrac{\arcsin(0.2)}{100\pi}$$ on my calculator (a Casio fx83) I get $$\displaystyle 6.4094 \times 10^{-4}$$

It does seem to be related to the way the calculator stores intermediate calculations - If I do $$\displaystyle \arcsin(0.2)$$ and save that to memory slot A and then do $$\displaystyle \frac{A}{100\pi}$$ I get $$\displaystyle 6.33 \times 10^{-3}$$

#### estex198

##### New member
Wow, that is interesting. I reset all RAM and ensured the OS was the latest version available from TI (1.19). Still getting same result. Perhaps its time to upgrade my adding machine... Thank you all for your help!

#### Ackbach

##### Indicium Physicus
Staff member
Wow, that is interesting. I reset all RAM and ensured the OS was the latest version available from TI (1.19). Still getting same result. Perhaps its time to upgrade my adding machine... Thank you all for your help!
Ok... Did you finally get the right result? If not, why are you marking the thread as solved? We're more than willing to keep helping you through...

#### estex198

##### New member
If the problem is due to a calculator error, what more is there to do? It looks as if the correct answer is 6.4094 * 10^-4. Thanks for your help!

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#### Ackbach

##### Indicium Physicus
Staff member
If the problem is due to a calculator error, what more is there to do?
Well, why don't you list the exact keystrokes you're using? Maybe there's something there we could look at.

#### estex198

##### New member
Ah. Ok. So going over the exact key strokes, it looks as if I wasnt putting 100pi in parenthesis. Looks like it was dividing 100 and then multiplying the result by pi. Sorry for wasting your time.