Gravitational acceleration, cosine problem

[BadatPhysicsguy]

Homework Statement

The gravitational acceleration at latitude x (0<x<90) can be estimated with g(x)=a*cos(2x)+b.
1) Determine what a and b is if the gravitational acceleration is 9.780m/s^2 at x=0 and 9.832m/s^2 at x=90.

Homework Equations

The Attempt at a Solution

So I begin by entering what I know:
9.780=a+b (Because cos(2*0) is 1)
9.780-a=b
And then the other equation:
9.832=-5.9846*a+b (Because cos(2*90) is -5.9846)

I then combine the two equations, jumping over the middle steps, gives:
-0.00868=a-a which means... -0.00868=0 which isn't logical. I wanted to get what a is, then enter it into either of the equations and get b.

 

[SteamKing]

Homework Statement

The gravitational acceleration at latitude x (0<x<90) can be estimated with g(x)=a*cos(2x)+b.
1) Determine what a and b is if the gravitational acceleration is 9.780m/s^2 at x=0 and 9.832m/s^2 at x=90.

Homework Equations

The Attempt at a Solution

So I begin by entering what I know:
9.780=a+b (Because cos(2*0) is 1)
9.780-a=b
And then the other equation:
9.832=-5.9846*a+b (Because cos(2*90) is -5.9846)

cos(2*90) = -5.9846? cosine can only evaluate between -1 and +1. Remember, latitude is measured in degrees, not radians. Try again.

 

[Mark44]

Homework Statement

The gravitational acceleration at latitude x (0<x<90) can be estimated with g(x)=a*cos(2x)+b.
1) Determine what a and b is if the gravitational acceleration is 9.780m/s^2 at x=0 and 9.832m/s^2 at x=90.

Homework Equations

The Attempt at a Solution

So I begin by entering what I know:
9.780=a+b (Because cos(2*0) is 1)
9.780-a=b
And then the other equation:
9.832=-5.9846*a+b (Because cos(2*90) is -5.9846)

You're skipping some steps here and writing stuff that isn't true. cos(2 * 90°) = -1.

I then combine the two equations, jumping over the middle steps, gives:
-0.00868=a-a which means... -0.00868=0 which isn't logical. I wanted to get what a is, then enter it into either of the equations and get b.

 

[BadatPhysicsguy]

cos(2*90) = -5.9846? Remember, latitude is measured in degrees, not radians. Try again.

Thank you! The book said that real life applications are measured in radians and not degrees, so I assumed it would be the same here. I solved it now, thanks again!

 

[SteamKing]

Thank you! The book said that real life applications are measured in radians and not degrees, so I assumed it would be the same here. I solved it now, thanks again!

Your book is not correct on this point. Latitude and longitude are always measured in degrees. In most other applications, degrees or grads are used. Radians are generally used only in math or science, because they simplify working with derivatives and integrals of trig functions.