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ISI MStat 2019 PSA Problem 15 | Trigonometry Problem

This is the problem from ISI MStat 2019 PSA Problem 15. First, try it yourself and then go through the sequential hints we provide.

Trigonometry - ISI MStat Year 2019 PSA Question 15


How many solutions does the equation \( cos ^{2} x+3 \sin x \cos x+1=0\) have for \( x \in[0,2 \pi) \) ?

  • 1
  • 3
  • 4
  • 2

Key Concepts


Trigonometry

Factorization

Check the Answer


Answer: is 4

ISI MStat 2019 PSA Problem 15

Precollege Mathematics

Try with Hints


Factorize and Solve.

\(\cos ^{2} x+3 \sin x \cos x + 1 = (2\cos x + \sin x)(\cos x +\sin x) = 0 \).
\( tanx = -2, tanx = -1 \).
Draw the graph.

Trigonometry problem graph - ISI MStat 2019 PSA Problem 15
Fig:1

So, if you see the figure you will find there are 4 such x for \( x \in[0,2 \pi) \).

Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

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