How do you use the angle sum or difference identity to find the exact value of cos(pi/3+pi/6)?

3 Answers
Jun 26, 2018

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

Therefore cos(pi/3+pi/6) turns into

cos(pi/3)cos(pi/6)-sin(pi/3)(sin(pi/6)

1/2*sqrt3/2-sqrt3/2*1/2 rarr 0

This makes sense as cos(pi/3+pi/6) rarr cos(pi/2) rarr 0

Jun 26, 2018

cos (pi/3 + pi/6) = 0

Explanation:

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

hat A = pi/3, hat B = pi/6

cos A = cos (pi/3) = 1/2, sin A = sin (pi/3) = sqrt3 / 2

cos B = cos (pi/6) = sqrt3 / 2, sin B = sin (pi/6) = 1 / 2

cos (pi/3 + pi/6) = ((1/2) * sqrt3/2) - (sqrt3/2 * (1/2)) = 0

Jun 26, 2018

cos (pi/3 + pi/6) = cos (pi/2) = 0

Explanation:

cos (pi/3 + pi/6)

=> cos ((2pi + pi) / 6 ) = cos (pi/2) = cos (90^@) = 0