Question

6sin216 разделить на sin 36

Answer 1

$sin216= sin( \pi +36)=-sin36$

$\frac{6*(-sin36)}{sin36}=-6$

Answer 2

To divide 6sin216 by sin36, we can use the trigonometric identity:

sin(A)/sin(B) = 2cos((A+B)/2)sin((A-B)/2)

Applying this identity, we have:

6sin216 / sin36 = 2cos((216+36)/2)sin((216-36)/2)

Simplifying further:

= 2cos(252)sin(90)

Since cos(252) = cos(360 - 252) = cos(108) and sin(90) = 1, we have:

= 2cos(108)

Now, we can use the unit circle or a calculator to find the value of cos(108):

cos(108) ≈ -0.30901699437

Therefore, 6sin216 / sin36 is approximately:

= 2cos(108) ≈ 2(-0.30901699437) ≈ -0.61803398874