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

Question

17pie/4

Answer 1

To find the reference number of t, we need to find the angle that has the same initial side as t and intersects the positive x-axis.

Since one full revolution is equal to 2π radians, we can subtract 2π from t until we get an angle between 0 and 2π.

17π/4 = (16π + π/4)

Since 16π is equivalent to 8 full revolutions (2π * 8 = 16π), we can ignore that part.

So, π/4 is the reference number of t.

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

For π/4, the cosine and sine of the angle can be found using the 45-45-90 triangle formed in the first quadrant of the unit circle.

Since the 45-45-90 triangle has sides in the ratio of 1:1:√2, the cosine and sine values for π/4 are both 1/√2.

Therefore, the terminal point determined by t is (1/√2, 1/√2).