This is the problem from ISI MStat 2019 PSA Problem 15. First, try it yourself and then go through the sequential hints we provide.
How many solutions does the equation \( cos ^{2} x+3 \sin x \cos x+1=0\) have for \( x \in[0,2 \pi) \) ?
Trigonometry
Factorization
But try the problem first...
Answer: is 4
ISI MStat 2019 PSA Problem 15
Precollege Mathematics
First hint
Factorize and Solve.
Second Hint
\(\cos ^{2} x+3 \sin x \cos x + 1 = (2\cos x + \sin x)(\cos x +\sin x) = 0 \).
\( tanx = -2, tanx = -1 \).
Draw the graph.
Final Step
So, if you see the figure you will find there are 4 such x for \( x \in[0,2 \pi) \).
This is the problem from ISI MStat 2019 PSA Problem 15. First, try it yourself and then go through the sequential hints we provide.
How many solutions does the equation \( cos ^{2} x+3 \sin x \cos x+1=0\) have for \( x \in[0,2 \pi) \) ?
Trigonometry
Factorization
But try the problem first...
Answer: is 4
ISI MStat 2019 PSA Problem 15
Precollege Mathematics
First hint
Factorize and Solve.
Second Hint
\(\cos ^{2} x+3 \sin x \cos x + 1 = (2\cos x + \sin x)(\cos x +\sin x) = 0 \).
\( tanx = -2, tanx = -1 \).
Draw the graph.
Final Step
So, if you see the figure you will find there are 4 such x for \( x \in[0,2 \pi) \).
