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 $x \in[0,2 \pi)$ .

Similar Problems and Solutions

Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

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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 $x \in[0,2 \pi)$ .

Similar Problems and Solutions

Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Related

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