jika sin α = 1/ akar 3, maka harga cesecα. tgα adalah ...

Bab Trigonometri
Matematika SMA Kelas X

sin a = 1/√3 

cosec a . tan a
= 1/sin a . sin a/cos a
= 1/cos a
= 1/(√(1 - sin² a)
= 1/(√(1 - (1/√3)²)
= 1/(√1 - 1/3)
= 1/(√(2/3))
= √3 / √2
= 1/2 √6

[tex]\displaystyle \sin a=\frac1{\sqrt3}\\y=1\\r=\sqrt3\\x=\sqrt{r^2-y^2}=\sqrt2\\\\\csc a\cdot\tan a=\frac{1}{\sin a}\cdot\frac{\sin a}{\cos a}\\\csc a\cdot\tan a=\frac{1}{\cos a}\\\csc a\cdot\tan a=\frac{r}{x}\\\csc a\cdot\tan a=\frac{\sqrt3}{\sqrt2}\\\boxed{\boxed{\csc a\cdot\tan a=\frac12\sqrt6}}[/tex]