The value of $\cos\left(-\frac{\pi}{2}\right)$ can be determined using the unit circle.

Understanding the Unit Circle

The angle $-\frac{\pi}{2}$ radians corresponds to a rotation of $\frac{\pi}{2}$ radians or $90^\circ$ in the clockwise direction from the positive x-axis.

Cosine at $-\frac{\pi}{2}$

On the unit circle:

• The angle $-\frac{\pi}{2}$ lands on the negative y-axis.
• The coordinates of this point are $(0, -1)$.

The cosine of an angle is the x-coordinate of the corresponding point on the unit circle. Since the x-coordinate is $0$ at $-\frac{\pi}{2}$,

$\cos\left(-\frac{\pi}{2}\right) = 0$

Would you like any further details or have any questions?

Related Questions:

1. What is the sine value at $-\frac{\pi}{2}$?
2. How do you find the cosine of any angle using the unit circle?
3. What is the general rule for cosine of negative angles?
4. How does the unit circle help in understanding trigonometric functions?
5. What are the values of cosine for standard angles (like $0$, $\frac{\pi}{4}$, $\frac{\pi}{2}$)?

Tip:

Remember that the cosine function is even, meaning $\cos(-\theta) = \cos(\theta)$, which can simplify the evaluation of cosine for negative angles.