Before You Begin

Question #40430

Difficulty: 8/10 | 🟢 Free

The Question

Let $\theta$ be an angle whose measure in degrees is $x$ and in radians is $y$ . Find the sum of all valid values of $y \in [0, 2\pi]$ that satisfy the equation: $\frac{\cos 3x + \cos 2x + \cos x}{\text{sgn}\left( 12y^2 - 11\pi y + 2\pi^2 \right)} = 0$

Options

A.
$\frac{61\pi}{12}$
B.
$6\pi$
C.
$\frac{23\pi}{4}$
D.
$\frac{16\pi}{3}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Radian-Degree Conversion Identity|Extraneous Solution Rejection|Signum Function Discontinuity

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to navigate between degree and radian measures while enforcing strict domain constraints imposed by the signum function.

A common trap is solving the numerator to find all roots but failing to check them against the denominator's signum argument.

Because sgn(0) = 0, any root that zeroes out the quadratic in the denominator leads to an undefined expression (division by zero).

Students who overlook this discontinuity will incorrectly include the extraneous roots (pi/4 and 2pi/3) in their final sum, leading directly to the trap options.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Trigonometric Functions - Class 11
Concept	Radian-Degree Conversion Identity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free