Eileen, Jackie, and Kathryn needed to find the difference between two angles A1 and A2, that they had drawn on a diagram:
B = A1+A2
They then had to find the cosine of B. Jackie measured A1 to be 50° and A2 to be 3°. But their pencil was kind of dull, so the lines they had drawn were about 0.5° thick. How much uncertainty in each angle was caused by the thick pencil lines? How much uncertainty is there in B? How about the cosine of B?
I found b(max) = 48 and b(min) to be 46 and the uncertainty to be 47+/- 1 but I don't know how to find cosine of B. Also is my answer for uncertainty correct?
To find the uncertainty caused by the thick pencil lines, you need to consider the measurement precision. In this case, the thickness of the pencil lines is about 0.5°. Since Jackie measured both angles A1 and A2, we can assume that each angle can be off by ±0.5° due to the thickness of the pencil lines.
Therefore, the uncertainty in each angle is ±0.5°.
To find the uncertainty in B, which is the sum of A1 and A2, you can simply add the uncertainties for both angles. This means the uncertainty in B is ±1°.
Now, to find the cosine of B, you need to use the actual values rather than the maximum and minimum values. Since Jackie measured A1 as 50° and A2 as 3°, you can calculate B as follows:
B = A1 + A2
B = 50° + 3°
B = 53°
Now, you can calculate the cosine of B using a scientific calculator or a mathematical software. The cosine function operates in radians, so you need to convert 53° to radians before calculating the cosine.
Cos(B) = cos(53°)
Using a scientific calculator or mathematical software, you can find the numerical value of the cosine of B.