Find the exact value

Question

A. cos 11π/12

 

B. cos 195^◦

Answer 1

A. cos11∏/12=165º   (180/12=15 and 11*15=165)

    cos165º=cos(45º+120º)

    looking on the unit circle and using one of the addition identities...

    cos(45º+120º)=cos45cos120-sin45sin120

                          =(√2/2)(-1/2)-(√2/2)(√3/2)

                          =(-√2/4)-(√6/4)

                          =(-√2-√6)/4

 

B. cos195º=cos(45º+150º)

    use the same reasoning as above and you get...

    cos45cos150-sin45sin150

    (√2/2)(-√3/2)-(√2/2)(1/2)

    (-√6/4)-√2/4)

    (-√6-√2)/4

   

Answer 2

cos(11π/12) = cos(9π/12 + 2π/12)

 

                   = cos(3π/4 + π/6)

 

                   = cos(3π/4)cos(π/6) - sin(3π/4)sin(π/6)

 

                   = (-√2/2)(√3/2) - (√2/2)(1/2) = (-√6 - √2)/4

 

cos195° = cos(135° + 60°) Proceed in a manner similar to the above.