Question
A student solved the equation Start Fraction sine 2 x over cosine x End Fraction equals 2, 0 less than or equals x less than or equals pi, and found an answer of Start Fraction pi over 2 End Fraction. Describe the student's error. simple sentances only
Answers
GPT-4o mini
The equation is \(\frac{\sin(2x)}{\cos(x)} = 2\). The student may have only considered \(x = \frac{\pi}{2}\) as a solution.
At \(x = \frac{\pi}{2}\), \(\sin(2x) = \sin(\pi) = 0\). Thus, the equation becomes \(\frac{0}{\cos\left(\frac{\pi}{2}\right)}\), which is undefined.
The student should have solved for other possible angles.
There may be other values of \(x\) that satisfy the equation.
The student should check for all solutions within the interval \(0 \leq x \leq \pi\).
At \(x = \frac{\pi}{2}\), \(\sin(2x) = \sin(\pi) = 0\). Thus, the equation becomes \(\frac{0}{\cos\left(\frac{\pi}{2}\right)}\), which is undefined.
The student should have solved for other possible angles.
There may be other values of \(x\) that satisfy the equation.
The student should check for all solutions within the interval \(0 \leq x \leq \pi\).