Tan(7π/4)
To find the value of tan(7π/4), we first need to understand what the tangent function represents and the unit circle
To find the value of tan(7π/4), we first need to understand what the tangent function represents and the unit circle.
The tangent function, denoted as tan(x), is one of the six trigonometric functions. It represents the ratio of the length of the side opposite to an angle to the length of the adjacent side in a right triangle. In terms of the unit circle, the tangent of an angle corresponds to the y-coordinate divided by the x-coordinate of a point on the unit circle.
Now, let’s determine the value of tan(7π/4):
1. Start by converting the angle 7π/4 from radians to degrees. To do this, multiply 7π/4 by (180/π) to get:
7π/4 * (180/π) = 315 degrees
2. Next, we need to place 315 degrees on the coordinate plane of the unit circle. The angle 315 degrees corresponds to the fourth quadrant, where both the x-coordinate and y-coordinate are negative.
3. To find the value of tan(7π/4), we divide the y-coordinate by the x-coordinate of the point corresponding to 315 degrees on the unit circle.
In the fourth quadrant, the x-coordinate is positive √2/2 (since it is negative, but we neglect the sign for the ratio), and the y-coordinate is negative √2/2.
Therefore, tan(7π/4) = (√2/2) / (-√2/2).
The √2/2 terms cancel out, leaving us with:
tan(7π/4) = -1.
Hence, tan(7π/4) is equal to -1.
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