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)
