For this case we have the following expression:
We must evaluate the expression, then:
If we enter the expression in a calculator we have that the decimal form is given by:
If we round the expression we have to:
The option that is closest is option A.
because it is only one decimal place if it was two decimal places it would be 0.02
43.18 u round up to become 43.20
To get the y-value for our point, plug pi/4 into the original as x
Then to find a slope, we need to get the derivative:
y'=-sin(x) (and plug in pi/4 as x to find the slope at this point)
So the tangent line is y-√2/2=-√2/2(x-pi/4)
Part 2: I'm not positive on this but I think you're supposed to use this tangent line to approximate the value at x=pi/2 and find the degree of error.
y=1.3 rounded to the nearest tenth
So since we know that cos(pi/2) is actually 0, the maximum value of error would be 1.3 (1.3-0=1.3)
Hope this helps