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Which inequality would result in the shaded solution on the unit circle to the right?

Which Inequality Would Result In The Shaded Solution On The Unit Circle To The Right class=

Sagot :

Answer: Choice B

Explanation:

Cosine is positive in quadrants I and IV, but quadrant IV isn't shaded in so we can rule out choice A.

Sine is positive in quadrants I and II. So far it looks like choice B could work. In fact, it's the answer because sin(pi/6) = 1/2 and sin(5pi/6) = 1/2. So if 0 ≤ sin(x) < 1/2, then we'd shade the region between theta = 0 and theta = pi/6; as well as the region from theta = 5pi/6 to theta = pi.

Choice C is ruled out because tangent is positive in quadrants I and III, but quadrant III isn't shaded.

Choice D is ruled out for similar reasoning as choice A. Recall that [tex]\sec(x) = \frac{1}{\cos(x)}[/tex]

Answer:

0 ≤ sin x < 1/2.

Step-by-step explanation:

sin π6 = 1/2

sin 5π/6 = 1/2

sin 0 and sin 180 = 0

The dotted line indicates that the value of the sine is less than 1/2 and the solid line indicates that value  is greater or equal to zero.

So the inequality is 0 ≤ sin x < 1/2

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