Question

The exact value of cos 17pi/8 is . . a) square root of 2+the square root of 2/4 . b.) 0.38. c.) 0.99. d.)square root of 2-the sqaure root of 2/4

Answer 1

Cos(17pi/8)

cos(17π/8)

But π radians = 180°

17π/8 radians = (17/8) * 180 = 382.5

But this is more than 360°,  so we have the basic angle by subtracting 360°

382.5 - 360 = 22.5

cos(17π/8) = Cos22.5

Recall double angle formula for cos.

cos2θ = 2cos²θ - 1

Therefore

cos(2*22.5) = 2cos²(22.5) - 1

cos45 = 2cos²(22.5) - 1

(√2)/2  =  2cos²(22.5) - 1

2cos²(22.5) - 1 =  (√2)/2


2cos²(22.5)  = (√2)/2 + 1

 2cos²(22.5)  = (2 + √2) / 2

cos²(22.5) = (2 + √2) / 4

cos22.5  =   √( (2 + √2)/4) ................(note)

cos22.5 = √(2 + √2) / 2

Option (a) seems like the closest, comparing to (note) above.