Question

Cos(38.1) = 0.7869350 What is the answer expressed to the correct number of significant figures. How do you know what the significant figures here?

Answer 1

`cos(38.1) = 0.787`

Explanation:

Assume that the measured angle is 38.1° ± 0.1°.

The calculated values of the cosines are

`cos(38.0) = 0.7880108`
`cos(38.1)= 0.7869350`
`cos(38.2) = 0.7858569`

The rule is that the values should differ only in one digit.

To 3 digits after the decimal place, the values become

`cos(38.0) = 0.788`
`cos(38.1) = 0.787`
`cos(38.2) = 0.786`

These differ only in the third digit after the decimal place, so the cosine of the measured angle 38.1° has three significant figures.

The cosine of the mathematical (exact) angle 38.1 ° has an infinite number of significant figures.