Question

Part 2: Using exact values, draw and direct the given angle on the given axis. Then, state the next positive and negative co-terminal angle. Use the extra space to show all your work. Angle = 3.56 radians Angle = 19" radians + angle = + angle = angle = - angle =

Answer 1

Part 2: Using exact values, draw and direct the given angle on the given axis. Then, state the next positive and negative co-terminal angle. Use the extra space to show all your work.

Angle = 3.56 radians 1-57 + angle = 9.84 3.56 3.14 6.28 angle = -2.72 A71

The quadrantal angles are 0, pi/2, pi, 3pi/2 and 2pi.
When pi=22/7, the values turn out to be 0, 1.57, 3.14, 4.71 and 6.28 respectively.
So 3.56 radians is in 3rd quadrant.
Also 7pi/6 = 3.66, so this value is too close to but slightly less than that as shown in the above figure.

Coterminal angles are angles with the same terminal side.
In radians, coterminal angles can be obtained by adding or subtracting multiples of 2pi to the given angle.
So the set of all angles coterminal with 3.56 is given by 3.56+2pi*n
+ coterminal angle = 3.56+2pi = 3.56 + 6.28 = 9.84 radians
- coterminal angle = 3.56-2pi = 3.56 - 6.28 = -2.72 radians

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10pi/3 is greater than 2pi and so it is 2pi + 4pi/3. So it takes one complete rotation of 2pi radians and an additional 4pi/3 radians as well.
It can also be done using the concept of the reference angle in the 3rd quadrant. Reference angle = 4pi/3 - pi = pi/3 measured from x-axis to the 3rd quadrant.

Coterminal angles are angles with the same terminal side.
In radians, coterminal angles can be obtained by adding or subtracting multiple of 2pi to the given angle.
So the set of all angles coterminal with 10pi/3 is given by 10pi/3+2pi*n
+ coterminal angle = 10pi/3+2pi = (10pi+6pi)/3 = 16pi/3 radians
Note : 10pi/3 - 2pi = 4pi/3 is also a positive coterminal angle. But as the question says next angle, we could choose 16pi/3
- coterminal angle = 10pi/3-4pi = (10pi-12pi)/3 = -2pi/3 radians