Question

cos bracket 11 pi upon 9 Radian bracket close

Answer 1

cos(11$\pi$/7)

=> cos{( 7$\pi$ + 4$\pi$)/7]

=> cos( $\pi$ + 4$\pi$/7)

=> -cos( 4$\pi$/7)

Answer 2

Cos[$\frac{11\pi}{9}]^{c}$ where c is the symbol of radian.

  → As, π radian  = 180° degrees

  → 11 π/9 radian = 180°× 11/9=20°× 11=220°

Cos(220°)= Cos(180°+40°)= -Cos 40°⇒ [220° lies in third quadrant, and in third quadrant cosine of any angle is negative.]

Cos(120°)=Cos(3×40°)=4 cos³40° - 3 Cos 40°[ Using the formula Cos 3A= 4 Cos³A- 3 CosA] where A=40°

→ -1/2=4x³ -3x

→-8 x³ + 6 x+1=0, here x=-Cos 40°

Drawing the graph of above equation and getting values of x are , x=-0.766,-0.174,0.94

But -Cos 40° =-0.766, other two are different roots when A=2nπ+a,where a=-40°,and n is any integer.

⇒Cos 220°=-Cos 40°=-0.7660(approx)