Answer:
B) cos(x) - sin(x) ≥ -1
Step-by-step explanation:
The given graph shows a sinusoidal curve and a horizontal line at y = -1 intersecting at two points over the interval 0 ≤ x ≤ 2π.
The provided answer options are trigonometric inequalities, where the left side represents the sinusoidal curve, and the right side represents the horizontal line.
The minimum and maximum values of the functions y = sin(x) and y = cos(x) are -1 and 1, respectively. As the graphed curve has a minimum greater than -1 and a maximum greater than 1, it cannot be either y = sin(x) or y = cos(x). Therefore, we can immediately discount the inequalities cos(x) ≥ -1 and sin(x) ≥ -1.
The curve intersects the y-axis at y = 1. So, when we substitute x = 0 into the left side of the inequality, it should equal 1.
Substitute x = 0 into cos(x) - sin(x), and sin(x) - cos(x):
[tex]\cos(0) - \sin(0)=1-0=1\\\\\sin(0) - \cos(0)=0-1=-1[/tex]
Therefore, the trigonometric inequality that the given graph can help solve is:
[tex]\LARGE\boxed{\cos(x) - \sin(x) \geq -1}[/tex]
