diketahui tan A =2/3 (A sudut lancip). nilai dari sin 2A=....

tan A = y/x = 2/3
x = 3
y = 2
r = √x² + y²
r = √3² + 2²
r = √9 + 4
r = √13

Sin A = y/r = 2/√13
                   = 2/13 √13

Cos A = x/r = 3/√13
                     = 3/13 √13

Sin 2A = 2 Sin A. Cos A
             = 2 (2/13 √13)(3/13 √13)
             = 156/169
             = 12/13 

semoga membantu dan jdikan jawaban terbaik ya

[tex] \tan (A) = \frac{2}{3} \\ \sin(A) = \frac{ 2}{ \sqrt{9 + 4} } = \frac{2}{\sqrt{13}} \\ \cos(A) = \frac{3}{\sqrt{9 + 4} } = \frac{3}{\sqrt{13}} \\ \\ \sin(2A) = 2 \sin(A) \cos(A) \\ = 2 \times \frac{2}{\sqrt{13}} \times \frac{3}{\sqrt{13}} \\ = \frac{12}{13} [/tex]

Atau cara ini:
[tex] \tan(A) = \frac{2}{3} \\ \frac{ \sin(A) }{ \cos(A) } = \frac{2}{3} \\ 3\sin(A) = 2\cos(A) \\ \\ \sin(2A) = 2 \sin(A) \cos(A) \\ = 3 { \sin }^{2} (A) \\ = 3( { \frac{2}{\sqrt{13}} )}^{2} \\ = 3( \frac{4}{13} ) \\ = \frac{12}{13} [/tex]