Question

Sin(t)=-(sqrt(2))/(2)

Answer 1

$\sin t = -\dfrac{\sqrt{2}}{2}\\\\\\\left[\begin{gathered}t = -\dfrac{\pi}{4} + 2\pi k\\\\t = -\dfrac{3\pi}{4} + 2\pi k\end{gathered}\ \ ,\ k\in\mathbb{Z}$

Answer 2

The equation sin(t) = -(√2)/2 represents a trigonometric equation. To find the solutions for t, we can use the properties of the sine function.

The value -(√2)/2 corresponds to the sine of certain angles in the unit circle. Specifically, it corresponds to the angles where the terminal side of the angle intersects the unit circle at the points (-1/√2, 1/√2) and (1/√2, -1/√2). These angles are π/4 and 5π/4 radians (45 degrees and 225 degrees) in the standard unit circle.

So, the solutions for t in the equation sin(t) = -(√2)/2 are:

t = π/4 + 2πn and t = 5π/4 + 2πn, where n is an integer.

These solutions cover all possible values of t that satisfy the equation sin(t) = -(√2)/2.