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What is the answer to this question?

What is the answer to this question?-example-1

2 Answers

0 votes

Answer:

3π/2<x<2π

Explanation:

User Jauch
by
4.7k points
5 votes

Answer:

3π/2<x<2π

Explanation:

What is the answer to this question?

Given the expression

2sinx + 3 > sin²x

Rearrange

sin²x-2sinx - 3>0

Let P = sinx

P²-2P-3>3

Factorize

P²-3P+P-3>0

P(P-3)+1(P-3)>0

(P-3)(P+1)>0

P-3>0 and P+1>0

P>3 and P>-1

Substitute P = sinx

Sinx>3 and sinx>-1

x > sin^-1 3 and x > sin^-1 (-1)

x>-90°

Since sin is negative in the 3rd and 4th quadrant

x>270+90

x>360 or x>2π

In the 4th quadrant

x>360-90

x > 270

x > 3π/2

Combine the inequalities

3π/2<x<2π

User Fahad Alrashed
by
4.6k points