Question
determine the sign of tan(7π/6) and the quadrant in which it lies.
Answers
Answered by
oobleck
sorry, tan(x) is positive in QIII
Answered by
GPT 3.5
To determine the sign of tan(7π/6), we need to find the value of tan(7π/6).
First, let's find the reference angle for 7π/6 by subtracting it from π, which is the angle on the unit circle that lies on the x-axis in the positive direction:
Reference angle = π - 7π/6 = (6π/6) - (7π/6) = -π/6
Since the reference angle is -π/6, tan(-π/6) is negative.
Now, let's determine the quadrant in which 7π/6 lies. The given angle 7π/6 is in the third quadrant because it is greater than π and less than 3π/2.
Therefore, tan(7π/6) is negative and the angle 7π/6 lies in the third quadrant.
First, let's find the reference angle for 7π/6 by subtracting it from π, which is the angle on the unit circle that lies on the x-axis in the positive direction:
Reference angle = π - 7π/6 = (6π/6) - (7π/6) = -π/6
Since the reference angle is -π/6, tan(-π/6) is negative.
Now, let's determine the quadrant in which 7π/6 lies. The given angle 7π/6 is in the third quadrant because it is greater than π and less than 3π/2.
Therefore, tan(7π/6) is negative and the angle 7π/6 lies in the third quadrant.
Answered by
GPT 3.5
Apologies for the mistake. You are correct.
To determine the sign of tan(7π/6), we need to find the value of tan(7π/6).
We know that tan(x) is positive in the third quadrant (QIII) and negative in the second quadrant (QII).
To determine the value of tan(7π/6), we can convert 7π/6 to its equivalent angle in the first revolution of the unit circle by subtracting 2π:
7π/6 - 2π = -5π/6
Now, let's find the equivalent angle with a positive value by adding 2π:
-5π/6 + 2π = 7π/6
So, tan(7π/6) has the same value as tan(7π/6) which is positive in QIII.
Therefore, tan(7π/6) is positive, and the angle 7π/6 lies in the third quadrant (QIII).
To determine the sign of tan(7π/6), we need to find the value of tan(7π/6).
We know that tan(x) is positive in the third quadrant (QIII) and negative in the second quadrant (QII).
To determine the value of tan(7π/6), we can convert 7π/6 to its equivalent angle in the first revolution of the unit circle by subtracting 2π:
7π/6 - 2π = -5π/6
Now, let's find the equivalent angle with a positive value by adding 2π:
-5π/6 + 2π = 7π/6
So, tan(7π/6) has the same value as tan(7π/6) which is positive in QIII.
Therefore, tan(7π/6) is positive, and the angle 7π/6 lies in the third quadrant (QIII).