Question

diketahui sin alfa = 5/13 dengan 90 derajat < alpha < 180 derajat
tentukan nilai tagen 1/2 alfa adalah​

Answer 1

Verified answer

Teigonometri

90° < a < 180° kuadran II

sin a = 5/13

cos a = - √(1 - sin² a)

cos a = - √(1 - (5/13)²)

cos a = - √((13²- 25)/13²)

cos a = - 1/13 √144

cos a = - 12/13

atau

tripel pythagoras → 5, 12, 13

tan (1/2 a)

= sin a / (1 + cos a)

= (5/13) / (1 - 12/13)

= (5/13) / (1/13)

= 5/1

= 5

atau

tan (1/2 a)

= (1 - cos a)/sin a

= (1 - (-12/13))/(5/13)

= (25/13) / (5/13)

= 25/5

= 5