# Thread: Find where the two graphs intersect.

1. ## Find where the two graphs intersect.

Hello. I'm currently having problems on trying to find the intersection point of these two trig graphs:

a(t) = -175cos(0.23t) - 75

b(t) = 172sin(0.23t) - 80

0 ≤ t ≤ 30

-----

Well, I assume this would be the first step:

-175cos(0.23t) - 75 = 172sin(0.23t) - 80

Now, I am finding it difficult to do the rest.

Looks like simple algebra to get the t by itself but it's proving to be harder than I anticipated.

I know the answers (using my graphics calculator to find the points) and they are:

(10.12,45.1) and (23.95,-200.19)

Any help is of course, appreciated.

Thankyou.

2. Originally Posted by sqleung
Hello. I'm currently having problems on trying to find the intersection point of these two trig graphs:

a(t) = -175cos(0.23t) - 75

b(t) = 172sin(0.23t) - 80

0 ≤ t ≤ 30

-----

Well, I assume this would be the first step:

-175cos(0.23t) - 75 = 172sin(0.23t) - 80

Now, I am finding it difficult to do the rest.

Looks like simple algebra to get the t by itself but it's proving to be harder than I anticipated.

I know the answers (using my graphics calculator to find the points) and they are:

(10.12,45.1) and (23.95,-200.19)

Any help is of course, appreciated.

Thankyou.
This is not able to be answered by conventional methods

Try the Newton-Raphson method

Newton's Method -- from Wolfram MathWorld

3. Originally Posted by sqleung
Hello. I'm currently having problems on trying to find the intersection point of these two trig graphs:

a(t) = -175cos(0.23t) - 75

b(t) = 172sin(0.23t) - 80

0 ≤ t ≤ 30

-----

Well, I assume this would be the first step:

-175cos(0.23t) - 75 = 172sin(0.23t) - 80

Now, I am finding it difficult to do the rest.

Looks like simple algebra to get the t by itself but it's proving to be harder than I anticipated.

I know the answers (using my graphics calculator to find the points) and they are:

(10.12,45.1) and (23.95,-200.19)

Any help is of course, appreciated.

Thankyou.
There are various ways of getting an exact answer (in the sense of writing the answer in the form t = arcsin(number), say). But before time is spent showing this, the question I'd like answered is the following:

Is an exact answer really required?

4. Guess that explains the reason why I couldn't get the answer. Newton's method is a little complex for me so I'll stick to technology.

Thankyou very much for your help.

5. Originally Posted by mr fantastic
There are various ways of getting an exact answer (in the sense of writing the answer in the form t = arcsin(number), say). But before time is spent showing this, the question I'd like answered is the following:

Is an exact answer really required?
No, the exact answer isn't required.