Find without using tables the values of Cosx and Sinx when Cos 2x is: 1/8 , 7/25 ,-119/169
I will do the 2nd one, you do the others.
given: cos 2x = 7/25
1 - 2sin^2 x = 7/25
2sin^2 x = 1-7/25 = 18/25
sin^2 x = 9/25
sinx = ± 3/25
sketch a right-angled triangle with height 3 and hypotenuse 25
then the adjacent side = √(625-9) = √616
if sinx = +3/25, then cosx = √616/25 , ( x = appr 6.9° ) quad I
or sinx = 3/25, then cos x = -√616/25 ( x= 173.1° ) quad II
if sinx = -3/25 , then cosx = -√616/25 (x = 186.9°) quad III
or sinx = -3/25 , then cosx = √616/25 (x = 353.1°) quad IV