find the exact value

Question

cosx = 12/13 

 

270<x< 360 

 

find sin(2x) 

Answer 1

x = cos^-1( 12/13) = 22.61 986495°

 

sin (2x) = 2sinxcosx

sin (2*22.61 986495°) = 2(sin22.61 986495°)(cos22.61 986495°)

0.71005917164579787941769433728693

 

How many decimal places?

 

 

Answer 2

X = cos^-1( 12/13) = 22.61 986495°

 

 Sin 2X = 2Sin X Cos X = 2 √( 1 - cos²X) . Cos X

 

                                    = 2 √(1 - 144/ 169) . 12/13

 

                                     = 2 . 5/13 . 12/13 = 120/ 169= 0.71