determine the value of cos (-pi/2) and explain the process
To determine the value of cos (-pi/2), we can use the unit circle and the definition of cosine.
The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It can be used to represent values of sine, cosine, and other trigonometric functions.
The definition of cosine is the x-coordinate of a point on the unit circle. Since we are looking for cos (-pi/2), we want to find the x-coordinate of the point on the unit circle that is pi/2 radians clockwise from the positive x-axis.
Starting from the positive x-axis, we move in a clockwise direction by pi/2 radians. This brings us to the negative y-axis. At this point, the x-coordinate is 0, so the value of cos (-pi/2) is 0.
In summary, cos (-pi/2) = 0.
To determine the value of cos(-π/2), we can first recall the unit circle, which is a circle with a radius of 1. In the unit circle, the angle -π/2 lies on the negative y-axis.
The cosine function measures the x-coordinate of the point where the angle intersects the unit circle. Since the angle -π/2 lies on the negative y-axis, the x-coordinate of that point is 0.
Therefore, cos(-π/2) = 0.
You can also verify this result by using the periodicity property of the cosine function. Since the cosine function repeats itself every 2π units, we can add or subtract multiples of 2π to the angle and obtain the same cosine value.
By adding 2π to -π/2, we get 3π/2. And cos(3π/2) can be determined from the unit circle as well, which also yields 0.
Thus, we confirm that cos(-π/2) is indeed equal to 0.