Question

Вычислите sin a/2 и cos a/2 если cos a = 1/8

Answer 1

$sin \dfrac{a}{2}= б\sqrt{ \dfrac{1-cosa}{2} }= б\sqrt{ \dfrac{1- \frac{1}{8} }{2} }= б\sqrt{ \dfrac{7}{16} }= б\dfrac{ \sqrt{7} }{4} \\ \\ cos \dfrac{a}{2}= б\sqrt{ \dfrac{1+cosa}{2} }=б \sqrt{ \dfrac{1+ \frac{1}{8} }{2} } = б\sqrt{ \dfrac{9}{16} }= б\dfrac{3}{4}$

Answer 2

Cosa = 1 - 2Sin²a/2                                  Cosa = 2Cos²a/2 - 1
2Sin²a/2 = 1 - Cosa = 1 - 1/8 = 7/8           2Cos²a/2 = Cosa + 1= 1 + 1/8 = 9/8
Sin²a/2 = 7/8 : 2 = 7/16                             Cos²a/2 =9/8 : 2 = 9/16
Sina/2 = + - √7/4                                       Cosa/2 = + - 3/4