Question

Вычислить sin( π/4 - a), если cos a= -3/5, a ∈ ( π/2 ;π)
даю сто балов

Answer 1

$\cos(a) = - \frac{3}{5} \\ \sin( \frac{\pi}{4} - a) = \sin( - a + \frac{\pi}{4} ) \\ \sin(x + \frac{\pi}{4} ) = \frac{ \sin(x) \sqrt{2} + \cos(x) \sqrt{2} }{2} \\ \sin( - a + \frac{\pi}{4} ) = \frac{sin( - a) \sqrt{2} + cos( - a) \sqrt{2} }{2}\ = \frac{ - sin(a) \sqrt{2} + cos( a) \sqrt{2} }{2} = \frac{ - \sqrt{1 - cos(a)} \sqrt{2} + cos( a) \sqrt{2} }{2} = \frac{ - 2 \sqrt{ \frac{1}{5} } + \frac{3}{5} }{2} = 0.3 - \sqrt{ \frac{1}{5} }$