(i)

Cos840° = Cos(2.360° + 120°) …………(using Cos(2ϖ + x) = Cosx)

= Cos(120°)

= Cos(180° - 60°)

= - Cos60° ……………(using Cos(ϖ - x) = - Cosx)

(ii) sin870° = sin(2.360° + 150°) ………….(using sin(2ϖ + x) = sinx)

= sin150°

= sin(180° - 30°) ………(using sin(ϖ - x) = sinx)

= sin30°

(iii)tan( - 120°) = - tan12 …….(tan( - x) = tanx)

= - tan(180° - 60°) ……. (in II quadrant tanx is negative)

= - ( - tan60°)

= tan60°

(iv)

= ………..(using cos( - x) = - cosx)

= ………...(using cos(2ϖ + x) = cosx)

=

(v)

……..(IV quadrant sinx is negative)

(vi)tan225° = tan(180° + 45°) …………(in III quadrant tanx is positive)

(vii)

.….(tan( - x) = - tanx)

…..(in IV quadrant tanx is negative)

(viii)sin( - 1230°) = sin1230° ………….(using sin( - x) = sinx)

= sin(3.360° + 150°)

= sin150°

= sin(180° - 30°) ………….(using sin(180° - x) = sinx)

= sin30°

(ix)cos495° = cos(360° + 135°) …………(using cos(360° + x) = cosx)

= cos135°

= cos(180° - 45°) ………….(using cos(180° - x) = - cosx)

= - cos45°