TriGOnometri
Rumus Jumlah sudut
Penjelasan dengan langkah-langkah:
Diketahui Cos A = 4/5 dan Sin B= -15 / 17
dengan A sudut dikuadran 1 dan B sudut di kuadaran III.
Tentukan nilai dari Tan (A + B)
cos A= 4/5
[tex]\sf \tan A = \pm \dfrac{\sqrt{5^2-4^2}}{4} =\pm \dfrac{3}{4}, < A \ di\ KD\ I, \tan A > 0[/tex]
[tex]\sf \tan A= \dfrac{3}{4}[/tex]
sin B = -15/17
[tex]\sf \tan B = \pm \dfrac{15}{\sqrt{17^2-15^2}} = \pm \dfrac{15}{8}, B \ di\ KD III, \tan B > 0[/tex]
[tex]\sf \tan \ B = \dfrac{15}{8}[/tex]
[tex]\sf \tan (A + B) =\dfrac{tan \ A + \tan B}{1 - tan \ A .tan \ B }[/tex]
[tex]\sf \tan (A + B) =\dfrac{\frac{3}{4}+ \frac{15}{8}}{1 - \frac{3}{4}. \frac{15}{8}}[/tex]
[tex]\sf*kalikan \frac{32}{32}[/tex]
[tex]\sf \tan (A + B) =\dfrac{32(\frac{3}{4}+ \frac{15}{8})}{32(1 - \frac{3}{4}. \frac{15}{8})}[/tex]
[tex]\sf \tan (A + B) =\dfrac{24+60}{32- 45} =\dfrac{84}{-13}[/tex]
[tex]\sf \tan (A + B) =-\dfrac{84}{13}= - 6\frac{6}{13}[/tex]
