Sets, Relations & Functions
Trigonometric Equation — Number of Solutions in [0,2π]
nta_pyq_2023_apr
Grade 11
Question:
The number of solutions of $3\cos^4\theta-5\cos^2\theta-2\sin^6\theta+2=0$ in $[0,2\pi]$
Step-by-Step Solution
Key Concept: Let $\sin^2\theta=t$. Factor: $(t-1)(2t^2-t)=0\Rightarrow t=0,\frac{1}{2},1$.
9 solutions.
Correct Answer: 4