Question

Find the reference angle of 17π/14.A ship starts at point P, travels 120 miles to point Q, adjusts its route according to the angle shown, and continues another 97 miles to point R. To the nearest mile, what is the distance from the starting position of the ship to its current position at point R?

Answer 1

The reference angle of 17π/14 is 11π/14.

Step-by-step explanation:

The reference angle of a given angle is the positive acute angle between the terminal side of the angle and the x-axis. To find the reference angle of 17π/14, we need to find the angle in the first quadrant that has the same terminal side as 17π/14. Since one full revolution is 2π, we can subtract 2π from 17π/14 to bring the angle to the first quadrant.

17π/14 - 2π = 17π/14 - 28π/14

= -11π/14

The reference angle is the absolute value of -11π/14, which is 11π/14.