Buku Sukino
Matematika Peminatan
Kelas XII
Bab Aplikasi Turunan
LKS 2
19. Persamaan garis normal pada kurva h(θ) = cosec θ pada titik berabsis θ = π/4 adalah ...
a. x√2 + y = √2 (π/4 + 1)
b. x√2 + y = √2 (π/4 + 1)
c. x - y√2 = (2 - π/4)
d. x - y√2 = √2 (2 - π/4)
e. x + y√2 = √2 (π/4 - 2)
Jawaban :
h(θ) = cosec θ
h'(θ) = - cosec θ . cotan θ
absis θ = π/4
h'(π/4) = - cosec π/4 . cotan π/4
h'(π/4) = - 1/sin π/4 . 1
h'(π/4) = - 1/(√2/2)
h'(π/4) = - √2
garis normal memiliki gradien : - 1 / m
m normal = -1/(- √2)
m normal = 1/2 √2
cari nilai h(π/4)
h(π/4) = cosec θ
h(π/4) = cosec π/4
h(π/4) = √2
titik : π/4, √2
persamaan garis normal
y - y1 = m normal (x - x1)
y - √2 = 1/2 √2 (x - π/4)
2y - 2√2 = √2x - √2 . π/4
√2x - 2y = √2 . π/4 - 2√2
√2x - 2y = √2 (π/4 - 2)
dikalikan √2 di kedua ruas
2x - 2√2 y = 2 (π/4 - 2)
dibagi 2
x - y√2 = (π/4 - 2)
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