Question

любые 6 Математика тригонометрия

Answer 1

1)

$3 \sin( \frac{\pi}{6} ) \tg( \frac{\pi}{4} ) = 3 \sin( \frac{\pi}{6} ) \times 1 = 3 \times \frac{ 1 }{2} = \frac{3}{2} = 1.5$

2)

$3 \sin( \frac{\pi}{6} ) - \tg( \frac{\pi}{4} ) + 2 \sin( \frac{\pi}{2} ) - \cos(\pi) = 3 \times \frac{1}{2} - 1 + 2 \times 1 - ( - 1) = \frac{3}{2} - 1 + 2 + 1 = 1.5 + 2 = 3.5$

3)

$\sin(0) + \cos( \frac{\pi}{2} ) + \sin( \frac{\pi}{4} ) = 0 + 1 + \frac{ \sqrt{2} }{2} = 1 + \frac{ \sqrt{2} }{2} = \frac{2 + \sqrt{2} }{2}$

4)

$\tg( \frac{23\pi}{4} ) \cos( \frac{23\pi}{3} ) \sin( \frac{23\pi}{6} ) = \tg( \frac{24\pi}{4} - \frac{\pi}{4} ) \cos( \frac{24\pi}{3} - \frac{\pi}{3} ) \sin( \frac{24\pi}{6} - \frac{\pi}{6} ) = \tg(6\pi - \frac{\pi}{4} ) \cos(8\pi - \frac{\pi}{3} ) \sin(4\pi - \frac{\pi}{6} ) = \tg( - \frac{\pi}{4} ) \cos( - \frac{\pi}{3} ) \sin( - \frac{\pi}{6} ) = - \tg( \frac{\pi}{4} ) \cos( \frac{\pi}{3} ) ( - \sin( \frac{\pi}{6} ) ) = 1 \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} = 0.25$

5)

$\frac{12 \sin(11°) \cos(11°) }{ \sin(22°) } = \frac{6 \times 2 \sin(11°) \cos(11°) }{ \sin(22°) } = \frac{6 \sin(2 \times 11°) }{ \sin(22°) } = \frac{6 \sin(22°) }{ \sin(22°) } = 6$

6)

$\tg(45°) \ctg(45°) = \frac{ \sin(45°) }{ \cos(45°) } \times \frac{ \cos(45°) }{ \sin(45°) } = 1$

7)

$3 \tg( \frac{\pi}{4} ) - \sin {}^{2} ( \frac{\pi}{3} ) + \cos {}^{2} ( \frac{\pi}{6} ) = 3 \times 1 - ( \frac{ \sqrt{3} }{2} ) {}^{2} + ( \frac{ \sqrt{3} }{2} ) {}^{2} = 3$

8)

$3 \sin( \frac{\pi}{6} ) + 2 \cos(\pi) + \ctg {}^{2} ( \frac{\pi}{6} ) = 3 \times \frac{1}{2} + 2 ( - 1) + ( \sqrt{3} ) {}^{2} = \frac{3}{2} - 2 + 3 = 1.5 + 1 = 2.5$