# Homework Help: Determine the equation for the the tangent

1. Sep 1, 2012

### Gliese123

1. The problem statement, all variables and given/known data
Determine the equation for the the tangent-to the curve:
y=3 sin 2x - cos 2x
if x=3∏/4

2. Relevant equations
So I thought I might get the y?

y=3 sin 2(3∏/4) - cos 2(3∏/4)
y= ~0.25 - ~1 ≈ 0.75

k(?) =
m(?) =
Then what?

3. The attempt at a solution

The answer is y = -2x + 3∏/2 - 3

Last edited: Sep 1, 2012
2. Sep 1, 2012

### rock.freak667

For y=3 sin2x - cos2x, how would you find the gradient function i.e. the function which gives the gradient at any point x?

3. Sep 1, 2012

### eumyang

This isn't correct. If you are using a calculator, are you sure you are in radian mode?

Once you get the correct y coordinate in the point, find the derivative of y. Plug x = 3π/4 into the derivative to get the slope of the tangent line. Finally, plug in the point and slope into the point-slope form of the equation of a line.

4. Sep 1, 2012

### Gliese123

I don't know really. Should I deriving?

5. Sep 1, 2012

### Gliese123

No I think its adjustments are set to angles. Is it possible to do it without setting it to radians?

6. Sep 1, 2012

### Bacle2

Do you know the definition of the derivative in terms of the tangent line?

This is what I think roc.freak was getting at.

7. Sep 1, 2012

### eumyang

You could also memorize the sine and cosine of special angles.
$y = 3 \sin \left(2 \cdot \frac{3\pi}{4}\right) - \cos \left(2 \cdot \frac{3\pi}{4}\right)$
$y = 3 \sin \left(\frac{3\pi}{2}\right) - \cos \left(\frac{3\pi}{2}\right)$
3π/2 is one such special angle. What is
$\sin \left(\frac{3\pi}{2}\right)$
and
$\cos \left(\frac{3\pi}{2}\right)$?

8. Sep 1, 2012

### Gliese123

When I put that on the calculator I get:
sin to be -0.99... and cos to be -2.38 × 10-3

9. Sep 1, 2012

### Gliese123

Should I take 3 × -0.9999 = -3. Is that the gradient?

10. Sep 1, 2012

### Gliese123

No. Sorry. I know how to derivate sin, cos etc. though

11. Sep 1, 2012

### eumyang

Something is wrong with your calculator. Because
sin (3π/2) = -1 and cos (3π/2) = 0.

No, it's not the gradient! It's the y-coordinate of the point where the tangent line intersects the curve. Please reread my post.

12. Sep 1, 2012

### Gliese123

Oh sorry! Hm. Okay so is y= -1 then? Sigh.. I don't know?
Should I derivate the function and put -1 = (the derivation)? (And include x)?

13. Sep 1, 2012

### eumyang

No, y does not equal -1. There was a 3 in front of the sine.

No again. You should take the derivative of
$y = 3 \sin 2x - \cos 2x$
$y' = ...$
and then plug in x = 3π/4. y' is the slope of the tangent line at x = 3π/4.

14. Sep 1, 2012

### Gliese123

So
y' = 3cos2x + 2sin2x right?
y' = 3 cos 2(3∏/4) + 2 sin 2(3∏/4) = - 4 ?
Could you lead me through please? I can't do this on my own.

15. Sep 1, 2012

### eumyang

No. You are forgetting the chain rule.

16. Sep 1, 2012

### Gliese123

I give up... Thanks very much for the help though.. :)

17. Sep 1, 2012

### HallsofIvy

The problem appears to be that you are trying to do a Calculus problem involving trig functions but have never learned Calculus or Trigonometry.

18. Sep 2, 2012

### Simon Bridge

It's in "homework" ... so it looks like OP is doing a course that requires calculus and trigonometry without having learned the prerequisites.

Actually, the question would be a good entry test for any situation where a basic understanding of calc and trig are required but not taught. Like a job interview.

19. Sep 2, 2012

### Gliese123

Yes. It's in "Homework" which means that I'm no pro on this one. I just started with the concept of derivations in trigonometry. I get that there're a lot of rules when one derivate functions including trigonometry. What have caused me to fail the calulations is because my calculator seem to not be set to the primary settings. I hoped that someone could more or less tell me the finnish. That would be helpful, not just telling me what's wrong all the time.

20. Sep 2, 2012

### Simon Bridge

You mean, "derivatives of trigonometric functions"?
Or, that your course is on the concepts of differentiating trigonometric functions?
"when one differentiates functions"
You don't need a calculator at all so this is not true.
That would be against the forum rules.

The idea is that you do your homework - we can help out where you get stuck but we will not do the work for you. Thing is, you have been stuck on everything. You do not know how a sine function varies with angle, and you don't know the chain rule. Both of these things were in an earlier part of your coursework.

Therefor: you have to go back over your course notes.