Q. - Universityku

$sf tan( alpha ) = frac{1}{3} to : blue{untuk : alpha : sudut : lancip}$

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tentukan nilai dari $sf green{ sin(2 alpha ) }$

Q.

Jawab:

tan A = 1/3 = d/s

d= 1 , s= 3

m² = d²+s²= 1 +9

m = √10

sin A= d/m = 1/√10

cos A = s/m = 3/√10

sin 2A = 2 sin A cos A

sin 2A = 2 . (1/√10) (3/√10)

sin 2A = 6/10 = 3/5

trigonometri

tan 2a = 2 tan a / (1 – tan² a)

tan a = 1/3

tan 2a

= 2(1/3) / (1 – 1/9)

= 2/3 / (8/9)

= 3/4

tripel pythagoras → 3, 4, 5

sin 2a = 3/5