Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>If \(x + \sin y = 2014\) and \(x + 2014\cos y = 2013\), where \(0 \le y \le \frac{\pi}{2}\), then find the value of \([x+y] - 2005\) (where \([\cdot]\) denotes greatest integer function).</p>
Step-by-Step Solution
Key Concept: Subtract the equations to eliminate one variable, then use trigonometric constraints to find exact values.
<p>Solve the system of equations by elimination and use the constraint on $y$ to determine the unique values of $x$ and $y$, then apply the greatest integer function.</p>
Correct Answer: 9