Find the angle between 0 and 2pi that is coterminal with negative one half pi; expressing the answer in radians in terms of pi.
2pi - pi/2 = 1.5pi = 3pi/2rad.
Well, let me put on my mathematical clown nose and help you out with that question!
So, we're looking for an angle between 0 and 2pi that is coterminal with -1/2 pi. Coterminal angles are angles with the same initial and terminal sides, but they can have different measurements.
To find the coterminal angle, we need to add or subtract a full revolution (2pi) or a multiple of it.
Starting with -1/2 pi, let's add 2pi to it:
-1/2 pi + 2pi = 3/2 pi
So, the angle that is coterminal with -1/2 pi is 3/2 pi, which is equivalent to 3/2 times pi radians.
Remember, in the world of clown math, we like to have a little fun with our answers. So, the answer in terms of pi is "Three halves of a delicious pi pie!" Enjoy!
To find the angle that is coterminal with negative one half pi, we can add a full revolution (2π) to the angle until it falls between 0 and 2π.
First, let's determine the coterminal angle:
Negative one half pi = -π/2
To make it positive, we can add 2π:
-π/2 + 2π = 3π/2
However, 3π/2 is not between 0 and 2π.
To express it in radians in terms of π within the range:
3π/2 can be written as (3/2)π.
Thus, the angle between 0 and 2π that is coterminal with negative one half pi, expressed in radians in terms of π, is (3/2)π.
To find the angle between 0 and 2π that is coterminal with -1/2π, we need to add a multiple of 2π to the angle -1/2π until we get an angle within the desired range.
First, let's determine how many multiples of 2π we should add. Since we want the angle to be coterminal with -1/2π, but within the range 0 to 2π, we need to find the closest multiple of 2π to -1/2π.
To do this, we divide -1/2π by 2π:
-1/2π ÷ 2π = -1/2
The result, -1/2, represents the number of complete revolutions (-1) and half (1/2) that need to be added to -1/2π to obtain an angle within the range 0 to 2π.
Let's calculate the coterminal angle by adding this value:
-1/2π + (-1/2)(2π) = -1/2π + (-1/2)(2π) = -1/2π - π = -3/2π
So the angle that is coterminal with -1/2π, within the range 0 to 2π, is -3/2π.
Now, since the question asks for the answer to be expressed in terms of π, we can express the angle as:
-3/2π = -3π/2
Therefore, the angle between 0 and 2π that is coterminal with -1/2π, in radians expressed in terms of π, is -3π/2.