To help solve the trigonometric inequality 2sin^2(x)+. cos(2x)-2<-1, Tracey successfully graphed the equations y=2sin^2(x) +cos(2x)-2 and y=-1 with her graphing calculator. Which of the following statements is true about the inequality?

a. There is no solution because even though you cannot see it, the graph of the equation y=2sin^2(x) +cos(2x) -2 is above the graph of the equation y=-1 for all values of x.
b. There is no solution because the graph of the equation y=2sin^2(x) +2cos(x)-2 is the same as the graph of the equation y=-1, so y=2sin^2(x) +2cos(x)-2 is never below y=-1.
c.There are an infinite number of solutions because even though you cannot see it, the graph of the equation y=2sin^2(x) +2cos(x)-2 is below the graph of the equation y=-1 for all values of x.
d.There are an infinite number of solutions because the graph of the equation y=2sin^2(x) +2cos(x)-2 is the same as the graph of the equation y=-1, so y=2sin^2(x) +2cos(x)-2 is never below y=-1.

Also, if you graph the equations on a graphing calculator, the lines are right on top of each other, so the first equation can't be less than -1, so no solutions

Answer Link

MrRoyal MrRoyal · Answer 2 · 2022-05-05T12:40:33+02:00

The true statement about the inequality graphs is (d)

How to determine the true statement?

The equations are given as:

y=2sin^2(x) +cos(2x)-2 and y=-1

When the above equations are plotted, both lines fall on each other.

This means that:

The equations y=2sin^2(x) +cos(2x)-2 and y=-1 have the same value.

So, we can conclude that the system of equations have infinite number of solutions

Hence, the true statement about the inequality graphs is (b)

Read more about sine and cosine graphs at:

https://brainly.com/question/13276558

#SPJ2