Trigonometry
System of trig equations — number of x values
MJAT_TS5_P1
Grade 12
Question:
**Paragraph (continued):** The number of values of $x\in[0,2\pi]$ when the system has a solution for permissible values of $a$, is:
Step-by-Step Solution
Key Concept: At $a=-1$: need $\sin x\cos 2y=1$ and $\cos x\sin 2y=0$. From first: $\sin x=1$ and $\cos 2y=1$, or $\sin x=-1$ and $\cos 2y=-1$. Case 1: $x=\pi/2$. Case 2: $x=3\pi/2$.
$\mathbf{2}$ values of $x$.
Correct Answer: 2