Question

Find the exact value of the given expression using a sum or difference formula.

1) sin345°
2) cos(11π)/12 ...?

Answer 1

sin (a - b) = sinacosb - sinbcosa
1) sin345° = sin (360 - 15) = sin360cos15 - sin15cos360= 0-sin15 *1=
sin345° = - sin15,

2) cos(11π) /12= - cos pi / 12 = cos ( - 4pi/12 +3pi/12)= cos (- pi/3 + pi/4) =
cos (-pi/3) cos pi/4) + sin (-pi/3) sin( pi/4) = sqrt6 /4 - sqrt2/ 4