Question
( 5 sin x-12 cos n+7 )
let ( quad 5=gamma cos alpha )
[
begin{array}{l}12=v sin alpha Rightarrow gamma gamma=sqrt{s^{2}+12^{2}}=13end{array}
]
( therefore 13left[frac{5}{13} sin n-frac{12}{13} cos nright]+7 )
( Rightarrow quad 13[cos alpha sin n-sin alpha cos n]+7 )
( Rightarrow quad 13 sin (alpha-x)+7 )
( therefore ) rin. when, ( sin (alpha-n)=-1 )
( Rightarrow sin x=-13+7=-6 )
( Rightarrow 4 a x=13+7=20 quad therefore ) ranse ( =[-6,20] )

find the range of the function 5 sin x - 12 cos ** > Solin Hint. Put 5 = r cos a and 12 = r sin a 13 and tan a = re a and 12 = r sin a
Solution
