A wheel turns (11) complete revolutions and then (\frac{2\pi}{3}) radians. What is the total angle in degrees?
Answer and explanation
Correct answer: (4080^\circ)
One complete revolution is \\(360^\\circ\\). Therefore, 11 complete revolutions produce \\(11\\times360^\\circ=3960^\\circ\\). The additional angle is \\(2\\pi/3\\) radians. Since \\(\\pi\\) radians equals \\(180^\\circ\\), this angle equals \\(2\\times180^\\circ/3=120^\\circ\\). Adding both parts gives \\(3960^\\circ+120^\\circ=4080^\\circ\\). Hence option C is correct.
The important point is that revolutions and radians must first be expressed in the same unit before they are added. The 11 turns are not 11 degrees; each full turn contributes 360 degrees. Similarly, \\(2\\pi/3\\) is one-third of a full half-turn, or 120 degrees. The total angle is therefore 4080 degrees, not 3960 degrees, which would omit the extra rotation. The supplied answer C and explanation are accurate.
Frequently asked questions
What is the correct answer to this question?
(4080^\circ)
Why is this the correct answer?
One complete revolution is \\(360^\\circ\\). Therefore, 11 complete revolutions produce \\(11\\times360^\\circ=3960^\\circ\\). The additional angle is \\(2\\pi/3\\) radians. Since \\(\\pi\\) radians equals \\(180^\\circ\\), this angle equals \\(2\\times180^\\circ/3=120^\\circ\\). Adding both parts gives \\(3960^\\circ+120^\\circ=4080^\\circ\\). Hence option C is correct.
The important point is that revolutions and radians must first be expressed in the same unit before they are added. The 11 turns are not 11 degrees; each full turn contributes 360 degrees. Similarly, \\(2\\pi/3\\) is one-third of a full half-turn, or 120 degrees. The total angle is therefore 4080 degrees, not 3960 degrees, which would omit the extra rotation. The supplied answer C and explanation are accurate.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
