If θ is in the second quadrant and its reference angle is π/9, what is the principal radian value of θ?
Answer and explanation
Correct answer: 8π/9
A reference angle is the acute angle between the terminal arm and the nearest x-axis. In the second quadrant, the terminal arm lies π radians from the positive x-axis minus the reference angle. Therefore θ = π − α, where α = π/9. Calculation gives θ = π − π/9 = 8π/9. This value lies between π/2 and π, confirming that it is in the second quadrant, and it is already the principal value in the standard interval [0, 2π). Hence option A is correct. The values 10π/9 and 17π/9 lie in the third and fourth quadrants, while 7π/9 does not satisfy π − π/9.
Frequently asked questions
What is the correct answer to this question?
8π/9
Why is this the correct answer?
A reference angle is the acute angle between the terminal arm and the nearest x-axis. In the second quadrant, the terminal arm lies π radians from the positive x-axis minus the reference angle. Therefore θ = π − α, where α = π/9. Calculation gives θ = π − π/9 = 8π/9. This value lies between π/2 and π, confirming that it is in the second quadrant, and it is already the principal value in the standard interval [0, 2π). Hence option A is correct. The values 10π/9 and 17π/9 lie in the third and fourth quadrants, while 7π/9 does not satisfy π − π/9.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Angles.
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