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

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( 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] )

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