For the following values of t find (a) the reference number of t and (B) the terminal point determined by t

7pie/3

1 answer

To find the reference number of t, we need to find an angle that is coterminal with 7π/3 and lies between 0 and 2π.

Since 2π is the entire circle, we can subtract 2π from 7π/3 until we obtain an angle between 0 and 2π.

7π/3 - 2π = π/3

Now, we have an angle of π/3.

To find the terminal point determined by t, we use the unit circle.

Since π/3 is in the first quadrant, we move counterclockwise from the positive x-axis by an angle of π/3.

This gives us the terminal point (cos(π/3), sin(π/3)) = (1/2, √3/2).

Therefore, for t = 7π/3, the reference number is π/3 and the terminal point is (1/2, √3/2).