cos-1

**terminator** · October 27th 2010, 02:34 PM

I try to find X from the cosine formula but it doesn't sound right

12sq = 8 sq + 5sq - 2x 8x 5cosX
144 = 64 + 25 - 80cosX
55 = -80cosX
x= cos^-1(-55/80)

I keep getting 2.328837092
Please help

**TKHunny** · October 27th 2010, 02:44 PM

Well, when you get the correct answer, you should quit. Why are you still streesing over it?

Would you be happier with $\pi - acos\left(\frac{11}{16}\right)$

Maybe you were expecting the answer in degrees? 133.433 deg

**terminator** · October 27th 2010, 03:04 PM

how did you get 133.433 deg?

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

**skeeter** · October 27th 2010, 03:41 PM

Originally Posted by terminator

how did you get 133.433 deg?

using degree mode in your calculator ...

$\displaystyle 180 - \arccos\left(\frac{11}{16}\right) \approx 133^\circ$

**HallsofIvy** · October 29th 2010, 02:02 PM

Originally Posted by terminator

I try to find X from the cosine formula but it doesn't sound right

12sq = 8 sq + 5sq - 2x 8x 5cosX
144 = 64 + 25 - 80cosX
55 = -80cosX
x= cos^-1(-55/80)

I keep getting 2.328837092
Please help

If you are thinking about x as being an angle ("cosine" is a function- just because you talk about cos(x) it does not necessarily mean that x is and angle) then x= 2.3288... radians.

Since $\pi= 3.14159...$ radians corresponds to 180 degrees, 2.3288 radians= 2.3288 (180/3.14159)= 133.433... degrees.

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