Question

If 0 equal( Picture)

Answer 1

`\sin(\theta) = -(\sqrt2)/(2)`

`\cos(\theta) = -(\sqrt2)/(2)`

Explanation:

The sine of any given angle on the unit circle is the y-coordinate of the point on the circle at the given angle.

The cosine of any given angle on the unit circle is the x-coordinate of the point on the circle at the given angle.

See the attached image for a labeled unit circle.

The point on the unit circle that is at angle 5π/4 is:

`\left(-(\sqrt2)/(2),-(\sqrt2)/(2)\right)`

This means that:

`\sin\left((5\pi)/(4)\right) = \cos\left((5\pi)/(4)\right) = \boxed{-(\sqrt2)/(2)}`