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# ¿Podrían resolverme estos problemas? Por favor

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1 - Sen(2x)=½ si 0<=x=>360. ¿Qué valores de x cumplen?

2 - K=log(A)-2 log(B)+3 log(C)-3 log(D). Simplificar.

21 ago. 2014

#1
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K=log(A)-2 log(B)+3 log(C)-3 log(D)

$${log}_{10}\left({\mathtt{A}}\right){\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{B}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{C}}\right){\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{D}}\right) = {\mathtt{K}}$$

$${\mathtt{K}} = {log}_{10}\left({\mathtt{A}}\right){\mathtt{\,-\,}}{log}_{10}\left({{\mathtt{B}}}^{{\mathtt{2}}}\right){\mathtt{\,\small\textbf+\,}}{log}_{10}\left({{\mathtt{C}}}^{{\mathtt{3}}}\right){\mathtt{\,-\,}}{log}_{10}\left({{\mathtt{D}}}^{{\mathtt{3}}}\right)$$

$${\mathtt{K}} = {log}_{10}\left({\frac{{{\mathtt{AC}}}^{{\mathtt{3}}}}{\left({{\mathtt{B}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{{\mathtt{D}}}^{{\mathtt{3}}}\right)}}\right)$$

22 ago. 2014
#2
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Sen(2x)=½ si 0<=x=>360. ¿Qué valores de x cumplen?

I am not sure about the translation on this one ?

sine(2x)=1/2

sine is positive so 1st and 2nd quadrants

0<=x<=360   ?

0<=2x<=720

sine 30 degrees = 1/2

2x = 30, 150, 390, 510

x = 15, 75, 195, 255 degrees

22 ago. 2014