Question #2043

If sinA=5/8 and cosB=4/7. And 90 is less than or equal to A which is less than 180 and -90 is less than B which is less than 0. What is the value of sin (A+B)?

Expert's answer

<img src="/cgi-bin/mimetex.cgi?\cos{A} = \sqrt{1-\sin^2{A}} = \sqrt{1-25/64} = \sqrt{39}/8 \\ \sin{B} = \sqrt{1-\cos^2{B}} = \sqrt{1-16/49} = \sqrt{33}/7 \\ \sin(A+B) = \sin{A}\cos{B}+ \sin{B}\cos{A} = \\ =\frac{5}{8} \frac{4}{7} + \frac{\sqrt{33}}{7} \frac{\sqrt{39}}{8}= \frac{3\sqrt{143}}{56}" title="\cos{A} = \sqrt{1-\sin^2{A}} = \sqrt{1-25/64} = \sqrt{39}/8 \\ \sin{B} = \sqrt{1-\cos^2{B}} = \sqrt{1-16/49} = \sqrt{33}/7 \\ \sin(A+B) = \sin{A}\cos{B}+ \sin{B}\cos{A} = \\ =\frac{5}{8} \frac{4}{7} + \frac{\sqrt{33}}{7} \frac{\sqrt{39}}{8}= \frac{3\sqrt{143}}{56}" />

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