What is the value of 4cos(2(0)) ?

4cos(2(0))

4 cos (2 (0))

4

Solution steps

4 cos (2 (0))

= 4 cos (2 \cdot 0)

Simplify

= 4 cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 4 \cdot 1

Simplify

= 4

cos (\frac{25 π}{4})

2 (sin (4) + cos (4) + 4 (cos (4) - sin (4)))

1 - \frac{sin ( 4 5 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

cos (arctan (2))

sin (\frac{2 π}{3}) - cos (\frac{π}{12}) + tan (\frac{5 π}{4})