Tan(3π/2)
The tangent function (tan) is a trigonometric function that relates the ratio of the sine and cosine of an angle
The tangent function (tan) is a trigonometric function that relates the ratio of the sine and cosine of an angle. In order to find the value of tan(3π/2), we first need to understand the unit circle and the values of sine and cosine for different angles.
The unit circle is a circle with a radius of 1 centered at the origin of a coordinate system. The angle is measured in a counterclockwise direction from the positive x-axis.
The angle 3π/2 is equivalent to 270 degrees. In the unit circle, this angle lies on the negative y-axis. At this angle, the cosine is 0 and the sine is -1, as indicated by the coordinates of the point where the angle intersects the unit circle.
Now, let’s calculate the tangent of 3π/2 using the definition of tangent:
tan(3π/2) = sin(3π/2) / cos(3π/2)
Substituting the values we obtained earlier:
tan(3π/2) = (-1) / 0
Since the denominator is zero, this means that tan(3π/2) is undefined.
In summary, the tangent of 3π/2 is undefined because the cosine of 3π/2 is zero, resulting in division by zero in the formula for tangent.
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