Question

Diket cot x = -4/3. Dan 90˚ < x < 180˚
Tentukan harga dari sin x-cos x / tan x- sec x

Answer 1

Cot x = 1 / tanx
1 / tanx = -4 / 3
-4 tanx = 3
tan x = - 3 / 4

tanx = depan / samping

dengan segitiga, maka didapatkan :
depan = 3
samping = 4
miring = 5

sin x = depan / miring
= 3 / 5
kuadran 2 = 3 / 5

cos x = samping / miring
= 4 / 5
kuadran 2 = - 4/5

tan x = - 3 / 4

sec x = 1 / cosx
= 1 / (4/5)
= 5 / 4
kuadran 2 = - 5/4

sinx - cosx / tanx - sec x
= ((3/5) - (-4/5)) / ((-3/4) -(-5/4))
= ((3/5) + (4/5)) / ((-3/4) + (5/4))
= (7/5) / (2/4)
= 28 / 10

Answer 2

Dengan cot x = x/y = -4/3
Maka,
x = -4 (Karena kuadran II)
y = 3
r = 5 [Phytagoras 3 dan -4]
Maka,