Maths Help

[xD_aQt]

Hi,

I've got two questions that I'm unsure of.
1) If cosh(x)=2.5, what is sinh(x) exactly?
2) If an angle is measured to be 0.4 radians, what is its sine?

Any help would be appreciated.
Thanks

[Gloamglozer]

With part a, I think you can use the trig identity:



Though I'm not sure.

[xD_aQt]

I'm not sure about that formula either, would it work for that particular question?

[m@tty]

Yes, you can use the formula. Also for 2) you have an angle of 0.4^c, to find the sine just evaluate sin(0.4)

[xD_aQt]

Oh okay, thanks guys!

[xD_aQt]

What's the difference between sinh(x), cosh(x), tanh(x) and sin(x), cos(x), tan(x) ?

[m@tty]

They're the hyperbolic functions - http://en.wikipedia.org/wiki/Hyperbolic_function

They're based off hyperbolae rather than a circle, as with sine, cosine and tangent

[taiga]

You can use trig identities to turn them into hyperbolic identities, generally involves swapping a minus sign somewhere

The rule for it is here:
http://mathworld.wolfram.com/OsbornesRule.html

There are some equations (that wiki page has them) that relate the two types of functions together.

like  sinh(iz) = i sinz

[xD_aQt]

need help on a questions

find dx/dt when x = (5+2t)^6t
I got 12t(5+2t)^(6t-1) but the calculator says (6ln(2x+5)+(12x/2x+5)).(2x+5)^6t

could someone please explain?

[moekamo]

if you had x^x, to differentiate you would have to log both sides and do it implicitly, here you do the same thing since you cant differentiate with respect t t since it is both a power and in the bracket:

[xD_aQt]

I see, cheers mate!

[xD_aQt]

I've got a differentiation question that I'm unsure of as I'm not sure how to solve it.
The question asks to use implicit differentiation to find dy/dx of 3(x^2)y+4x(y^2)=5x-7

[brightsky]

3x^2y + 4xy^2 = 5x - 7
Use chain rule:
y*6x + y' * 3x^2 + 4 * y^2 + 4x * 2yy' = 5
6xy + 3x^2y' + 4y^2 + 8xyy' = 5
y'(3x^2 + 8xy) = 5 - 6xy - 4y^2
y' = (5 - 6xy - 4y^2)/(3x^2 + 8xy)
hope there's no errors.

edit: arithmetic error

[xD_aQt]

Just out of curiousity also, how would you solve it on the T.I. NSpire?

[xD_aQt]

A red car is travelling east towards an intersection at a speed of 40km/hr while a blue car is simultaneously travelling north towards the intersection at a speed of 60km/hr if the red car is 6km from the intersection and the blue car is 8km from the intersection at what rate is the distance between the cards changing?