Question

8/sin(-27П/4)cos(31П/4)

Answer 1

Ответ:

-16.

Пошаговое объяснение:

$\frac{8}{sin(-\frac{27\pi }{4})*cos(\frac{31\pi }{4} ) } = \frac{8}{-sin (6\pi +\frac{3\pi }{4})*cos (8\pi -\frac{\pi }{4} ) } = \frac{8}{-sin \frac{3\pi }{4} *cos\frac{\pi }{4} } =\\\\-\frac{8}{\frac{\sqrt{2} }{2} *\frac{\sqrt{2} }{2} } =-\frac{8}{0,5} =-16.$

Answer 2

The expression you provided is:

8/sin(-27π/4)cos(31π/4)

To simplify this expression, let's first evaluate the trigonometric functions.

sin(-27π/4) = sin(-6π + π/4) = sin(π/4) = √2/2

cos(31π/4) = cos(8π - π/4) = cos(7π/4) = -√2/2

Now we substitute these values back into the expression:

8 / (√2/2) * (-√2/2)

To divide by a fraction, we can multiply by its reciprocal:

8 * (2/√2) * (-2/√2)

Simplifying further:

8 * 2 * (-2) / (√2 * √2)

= -32 / 2

= -16

Therefore, the simplified value of the expression 8/sin(-27π/4)cos(31π/4) is -16.