Answer:
step 2
and then step 3 : the error neutralized the error of step 2
Step-by-step explanation:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
and because
sin(-b) = -sin(b)
cos(-b) = cos(b)
we have
sin(a - b) = sin(a)cos(-b) + cos(a)sin(-b) =
= sin(a)cos(b) - cos(a)sin(b)
3pi/2 = 270° or -90°.
sin(3pi/2) = sin(270) = sin(-90) = -1
that means, it is the full radius straight down from the center of the circle.
cos(3pi/2) = cos(270) = cos(-90) = cos(90) = 0
so, step 1 is correct :
sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2) =
= sin(A)×0 - cos(A)×(-1) (correct step 2)
but as we see, the provided step 2 is incorrect.
it should have been the indicated
sin(A)×0 - cos(A)×(-1)
and NOT the provided
sin(A)×0 + cos(A)×(-1)
step 3 based on the erroneous step 2 should then have been
sin(A)×0 - (1)cos(A)
but instead another error with the sign was made that neutralized the error of step 2 and we got after this second mistake by pure chance the overall correct step 3
sin(A)×0 + (1)cos(A)
so, again, the first error was made in step 2.
but technically, there was also a consecutive error made in step 3 to bring everything back to the correct approach.
