Question

Part 1: Find the tangent line approximation to cos x at x=π/4.

Answer 1

Part 1: To find the tangent line, we need a point and a slope because we are using point slope form: y-y1=m(x-x1)
To get the y-value for our point, plug pi/4 into the original as x
y=cos(x)
y=cos(pi/4)
y=√2/2
Then to find a slope, we need to get the derivative:
y=cos(x)
y'=-sin(x) (and plug in pi/4 as x to find the slope at this point)
=-sin(pi/4)
=-√2/2

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-√2/2=-√2/2(pi/2-pi/4)
y=-pi√2/8+√2/2
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