Find the reference number and the terminal point determined by t.
a. t = - 7(pi)/6
t = -7(pi)/6.
-7(pi)/6 * 180/(pi) = -210 deg.
-210 is 210 deg CW from the + x-axis
and is in the 2nd quadrant.
Ar = [-210] - 180,
Ar = 210 - 180 = 30 deg.
A = 180 - 30 = 150 DEG CW FROM +X AXIS.
To find the reference number and terminal point determined by t = -7(pi)/6, we need to first understand the concept of the unit circle.
The unit circle is a circle with a radius of 1 unit and its center at the origin (0, 0) of the coordinate plane. It is commonly used in trigonometry to define the values of trigonometric functions for different angles.
To determine the reference number, we find the equivalent angle in the unit circle's first rotation (0 to 2π or 0 to 360 degrees). In this case, since t = -7(pi)/6, we need to find an equivalent angle in the first rotation.
To convert an angle in radians to an angle in degrees, we use the fact that π radians is equal to 180 degrees. So, we can multiply -7(pi)/6 by 180/π to convert it to degrees.
-7(pi)/6 * (180/π) ≈ -210 degrees
Therefore, the reference number for t = -7(pi)/6 is -210 degrees.
To find the terminal point determined by t = -7(pi)/6, we need to locate the angle on the unit circle. Starting from the positive x-axis (the rightmost point on the unit circle), we move clockwise by 210 degrees.
Moving clockwise by 210 degrees corresponds to a rotation of (210/360) * 2π radians. Simplifying, we have:
(210/360) * 2π = 7(pi)/6
Thus, the terminal point determined by t = -7(pi)/6 on the unit circle is (cos(7(pi)/6), sin(7(pi)/6)). Evaluating these trigonometric functions:
cos(7(pi)/6) = -√3/2
sin(7(pi)/6) = -1/2
Therefore, the terminal point determined by t = -7(pi)/6 is (-√3/2, -1/2) on the unit circle.