Solve for: 12cos((16pi)/(3))+6sin((pi)/(6))

Expression: $12\cos\left({\frac{ 16π }{ 3 }}\right)+6\sin\left({\frac{ π }{ 6 }}\right)$

Calculate the trigonometric value

$12 \times \left( -\frac{ 1 }{ 2 } \right)+6\sin\left({\frac{ π }{ 6 }}\right)$

Use the trigonometric values table or unit circle to evaluate the expression

$12 \times \left( -\frac{ 1 }{ 2 } \right)+6 \times \frac{ 1 }{ 2 }$

Multiplying a positive and a negative equals a negative: $\left( + \right) \times \left( - \right)=\left( - \right)$

$-12 \times \frac{ 1 }{ 2 }+6 \times \frac{ 1 }{ 2 }$

Cancel out the greatest common factor $2$

$-6+6 \times \frac{ 1 }{ 2 }$

Cancel out the greatest common factor $2$

$-6+3$

Calculate the sum

$-3$