The exact value of cos 13pi/8 is

answer is : Cos (13pi/8) = 0.3826

Step-by-step explanation:

We have, Cos (13pi/8)

Since 13pi/8 can be shown as 3pi/2 < 13pi/8 < 2pi

Hence 13pi/8 lies on fourth quadrant.

In fourth quadrant cosine will be positive.

Cos (13pi/8) = cos (3pi/2 + pi/8)

applying formula cos (A+B) = cos A cosB - sinAsinB

i. e Cos (3pi/2 + pi/8) = cos (3pi/2) cos (pi/8) - sin (3pi/2) sin (pi/8)

∵ Remember cos (3pi/2) = 0, sin (3pi/2) = - 1

Cos (3pi/2 + pi/8) = 0 cos (pi/8) - (-1) sin (pi/8)

Cos (3pi/2 + pi/8) = 0 + 0.3826

Cos (3pi/2 + pi/8) = 0.3826

Hence we got Cos (13pi/8) = 0.3826

sqt root 2-sqt root 2/4