Question

Jika a = 105° dan b = 15°
Tentukan nilai dari
Sin 2a
Cos 2a
Tab 2a

Answer 1

tan \: a = - \frac{2}{3} \\ \frac{x}{y} = - \frac{2}{3} \\ r = \sqrt{ {2}^{2} + {3}^{2}} = \sqrt{4 + 9} = \sqrt{13}

sin \: a = \frac{x}{r} = \frac{2}{ \sqrt{13}} = \frac{2}{13} \sqrt{13}

cos \: a = \frac{y}{r} = - \frac{3}{ \sqrt{13}} = - \frac{3}{13} \sqrt{13}

jadi:

sin \: 2a = 2 \times sin \: a \times cos \: a \\ = 2 \times(\frac{2}{13} \sqrt{13}) \times ( - \frac{3}{13} \sqrt{13}) \\ = \frac{12}{13}

cos \: 2a = {cos}^{2} a - {sin}^{2} a \\ = {( - \frac{3}{13} \sqrt{13}})^{2} - {( \frac{2}{13} \sqrt{13}})^{2} \\ = \frac{9}{13} - \frac{4}{13} = \frac{5}{13}

tan \: 2a = \frac{2 \times tan \: a}{1 - {tan}^{2} a} \\ = ( + tan \: a) \div (1 - {tan}^{2} a) \\ = 2 \times (- \frac{2}{3} ) \div (1 - {( - \frac{2}{3})}^{2} \\ = - \frac{4}{3} \div (1 - \frac{2}{9} ) \\ = - \frac{4}{3} \div \frac{7}{9} \\ = - \frac{4}{3} \times \frac{9}{7} \\ = \frac{12}{7} = 1 \frac{5}{7}

Simak lebih lanjut di Brainly.co.id - brainly.co.id/tugas/15492035#readmore