Use an appropriate identity to find the exact value of the expression. COS (-17pi/12)?

Answer 1

Note that cos(-17pi/12) = cos(17pi/12) because cosine is an even function.

You want to break up 17pi/12 into two pieces and use the sum/difference formula for cosine.

After some guess & check work,

cos(17pi/12)

= cos(5pi/3 - pi/4)

= cos(5pi/3)cos(pi/4) + sin(5pi/3)sin(pi/4)

= 1/2 * sqrt(2)/2 + -sqrt(3)/2 * sqrt(2)/2

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

Answer 2

cos (-17pi/12)
= cos (-17pi/12 + 2pi)
= cos(7pi/12)
= cos(pi/3 + pi/4)
= cos(pi/3)cos(pi/4) - sin(pi/3)sin(pi/4)
= (1/2)(√2/2) - (√3/2)(√2/2)
= (√2 - √6) / 4

Answer 3

cos (-17 pi /12)
cos [ (-12 - 5 )pi /12 ]
cos [ -pi - 5 pi/12 ]
cos [ - 180 - 5 (180/12) ]
cos [ - 180 - 5 (15) ]
cos [ -180 - 75]
- cos 75

Answer 4

COS (-17π/12) =
- COS (5π/12) = (cos(π - x) = - cos(x))
- SIN (6π/12 - 5π/12) = (sin(π/2 - x) = cos(x))
- SIN (π/12) = - 1/2 or - 0.5