# Need help on this tricky question

• Aug 20th 2010, 05:16 AM
JohnLord123
Need help on this tricky question
Find the sum: Cos^2 (0) + Cos^2 (2) + Cos^2 (4) + Cos^2 (356) + Cos^2 (358) + Cos^2 (360)

• Aug 20th 2010, 10:02 AM
earboth
Quote:

Originally Posted by JohnLord123
Find the sum: Cos^2 (0) + Cos^2 (2) + Cos^2 (4) + Cos^2 (356) + Cos^2 (358) + Cos^2 (360)

1. I assume that the argument of the trigonometric functions is in degree (?).

2. You can simplify the given term a little bit:

Since

$\displaystyle \cos^2(0^\circ) = \cos^2(360^\circ) = 1$

$\displaystyle \cos^2(2^\circ) = \cos^2(358^\circ)$

$\displaystyle \cos^2(4^\circ) = \cos^2(356^\circ)$

you'll get:
$\displaystyle \begin{array}{l} \cos^2 (0^\circ) + \cos^2 (2^\circ) + \cos^2 (4^\circ) + \cos^2 (356^\circ) + \cos^2 (358^\circ) + \cos^2 (360^\circ)=\\ 2 + 2\cos^2(2^\circ)+2\cos^2(4^\circ)\end{array}$

Since $\displaystyle 2\cos^2(2^\circ) = \cos(4^\circ)+1$ the term simplifies to:

$\displaystyle 2+1+ \cos(4^\circ)+2\cos^2(4^\circ) = \boxed{3+ \cos(4^\circ)(1+2\cos(4^\circ))}$