Acceleration due to Gravity problem.

[sirajoman]

Homework Statement

Acceleration due to gravity, g, is considered to be 9.8(m/s^2). However, changes in latitude alter g according to the following model:
g = 9.78049(1 + 0.005288sin^2x-0.000006sin^2(2x))(m/s^2), where x is latitude measured in degrees.
[Side note= Hey guys i didn't know how to type in the little zero with the line across it which is the variable for degrees so i just used x, so x = zero-with-slash]

a) Rewrite g in terms of powers of sinx only
b)Find the latitude of Portland, Maine, and determine g.
c)Find the percent of change between the value calculated in part b above and the standard value of 9.8.

Homework Equations

I seriously can't think of any! I don't even know where to begin! :(

The Attempt at a Solution

Please excuse my sorry attempt:
a)1.g = 9.78049(1 + 0.005288sin^2x-0.000006sin^2(2x))(m/s^2)
2.g = 9.78049(sin0x +sin^2x-sin^2x)
3.g = 9.78049(sin^3x)
b)Using a calc to graph
portland = 5.4 degrees
g = 95
(im probably way off)
c)5.4/9.8 = .548

 

[Dick]

To write this as a power of sin(x) only, you just need to get rid of the sin(2x) term. Do you know a trig identity that will get you an expression for sin(2x) in terms of sin(x) and cos(x)? Then to write the cos(x) in terms of sin(x) remember 1=sin^2(x)+cos^2(x).

 

[BrendanH]

Dick is right. And for that 'zero with a slash in it', you mean the Greek letter 'phi' or 'theta' ;)

 

[ll Source ll]

Thanks Dick, you helped me out a lot i just have one small question though.
Sin^2(x) * sin^2(x) = sin^4(x) ...right? :)

Or anyone else, in case Dick isn't here could answer.

 

[Dick]

That's a really small question. Sure. x^2*x^2=x^4. So sin^2(x)*sin^2(x)=sin^4(x). How could you doubt it? Were you working on the same question as sirajoman?