Question

To solve the trigonometric inequality sin?(x) -0.85, Carl graphed the equations y=sin(x) and y=-0.85. Shelly, on the other
hand, took the cube root of both sides of the inequality so that it became sin(x) = -0.85, and she then graphed the equations
y = sin(x) and y -0.85. Which of the following statements is true regarding the points of intersection of Carl's graph and
Shelly's graph?

A The points of intersection of Carl's graph have different x-coordinates than the points of intersection of Shelly's graph and
different y-coordinates.

B The points of intersection of Carl's graph have different x-coordinates than the points of intersection of Shelly's graph but the
same y-coordinates.

C The points of intersection of Carl's graph have the same x-coordinates as the points of intersection of Shelly's graph but
different y-coordinates.

D The points of intersection of Carl's graph have the same x-coordinates as the points of intersection of Shelly's graph and the
same y-coordinates.

Answer 1

Answer: C

Step-by-step explanation:

The points of intersection of Carl’s graph have the same x-coordinates as the points of intersection of Shelly’s graph but different y-coordinates.

Answer 2

Trigonometric expressions can be represented using inequalities

The true statement is (c) the points of intersection of Carl’s graph have the same x-coordinates as the points of intersection of Shelly’s graph but different y-coordinates.

The inequality is given as:

$\mathbf{sin^3(x) < -0.85}$

The steps Carl took will give the following coordinates (x, y^3)

The steps Shelly took will give the following coordinates (x, y)

This means that, their results will have the same x-coordinates but different y-coordinates.

Hence, the true option is (c)

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