Question

Diketahui sin x + cos x = 1 dan tan x = 1, tentukan nilai sin x dan cos x

Answer 1

Tan x = 1
sin x + cos x = 1
bagi kedua ruas dengan cos x
sin x/cos x + cos x/cos x = 1/cos x
tan x + 1 = sec x
1 + 1 = sec x
2 = sec x
2 = 1/cos x
cos x = 1/2

sin x = √(1 - cos²x)
= √(1 - (1/2)²)
= √(1 - 1/4)
= √(3/4)
= 1/2 √3

Answer 2

Tanx = depan/samping

depan/samping = 1
depan = samping

depan/miring + samping/miring = 1
2depan/miring = 1
2depan = miring
depan = miring/2

misal, depan = 1

depan = miring/2
2depan = miring
miring = 2

sinx = depan/miring
= 1/2

samping = √(2² - 1²)
= √3

cosx = √3/2