Question

Mohon bantuannya.. Turunan fungsi trigonometri

Answer 1

g(x) = (cos[x-π/2])/(sin[x+π/4])

m = g'(x) = (-sin[x-π/2].sin[x+π/4] - cos[x+π/4].cos[x-π/2])/(sin[x+π/4])²

       = -(sin[x-π/2])/(sin[x+π/4]) - cot[x+π/4].sec[x+π/4] . cos[x-π/2]

g'(π/2) = -(sin[π/2-π/2])/(sin[π/2+π/4]) - cot[π/2+π/4].sec[π/2+π/4] . cos[π/2-π/2]

          = -cot[3π/4].sec[3π/4].cos 0

          = - cos[3π/4]/sin²[3π/4] . 1

         = - (-1/2 √2) / (1/2 √2)²

         = 1/(1/2 √2)

          = 2/√2

         = 2/√2 . √2/√2

m       =  √2

persamaan garis singgung di titik C(π/2 , √2)

y - y1 = m(x-x1)

y - √2 = √2(x-π/2)

y = √2 . x - π/2  √2  + √2

y = √2 . x + √2 (1 - π/2)   (B)