Ina sine bar, let h denote height of slip gauge and l be the distance between the rollers. The relationship between error in angular measurement (dθ) and errors in the slip gauge combination (dh) and in the spacing of the rollers (dl) is

1
\(\rm d\theta=sin\ \theta\left( \dfrac{dh}{h}-\dfrac{dl}{l}\right)\)
2
\(\rm d\theta=cos\ \theta\left( \dfrac{dh}{h}-\dfrac{dl}{l}\right)\)
3
\(\rm d\theta=tan\ \theta\left( \dfrac{dh}{h}-\dfrac{dl}{l}\right)\)
4
\(\rm d\theta=cot\ \theta\left( \dfrac{dh}{h}-\dfrac{dl}{l}\right)\)

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