Solving Sine Inequalities with Unit Circle

The video tutorial explains how to solve the inequality sin(x) ≥ -√3/2 using a four-step rule. It begins with drawing and labeling the unit circle, then indicates the sine values that meet the condition. The tutorial continues by identifying the arc on the circle where these values are valid and concludes by finding the specific values for points A and B. The final answer is presented in the form of an inequality, considering periodicity.

What is the inequality that needs to be solved in the video?

• cos(x) ≥ -√3/2

• sin(x) ≥ -√3/2

• sin(x) ≤ -√3/2

• cos(x) ≤ -√3/2

What is the first step in solving the inequality?

• Labeling the axes

• Finding the sine value

• Drawing the unit circle

• Calculating angles

What is the significance of the unit circle in this context?

• It is used to visualize sine values

• It is used to determine the distance between points

• It helps in finding cosine values

• It helps in calculating tangent values

In the second step, what value is indicated on the unit circle?

• One

• Zero

• Negative √3/2

• Positive √3/2

What is the purpose of identifying the arc in the third step?

• To calculate tangent values

• To find the range where sine values are greater than or equal to -√3/2

• To determine where sine values are less than -√3/2

• To find cosine values

What direction is considered positive in the fourth step?

• Upward

• Counterclockwise

• Downward

• Clockwise

What quadrant is point A located in?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the angle for point A?

• -60°

• 120°

• 240°

• 60°

What is the angle for point B?

• 240°

• 180°

• 120°

• 60°

How is the final inequality expressed?

• a ≥ x ≥ b

• a > x > b

• a ≤ x ≤ b

• a < x < b