Understanding Inequalities and Their Graphs

The video tutorial explains how to solve trigonometric inequalities, focusing on cosine and tangent functions. It begins with setting equations to zero, solving for critical values, and using test points or graphs to determine solution intervals. The tutorial covers both algebraic and graphical methods, emphasizing the importance of understanding quadrants and reference angles. It also addresses handling asymptotes in tangent inequalities.

What is the first step in solving an inequality?

• Set the inequality to zero

• Divide both sides by the variable

• Multiply both sides by two

• Subtract one from both sides

When solving cosine inequalities, in which quadrants is cosine positive?

• Quadrant III and IV

• Quadrant II and III

• Quadrant I and IV

• Quadrant I and II

What is the reference angle when cosine is equal to one-half?

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees

How do you represent an open circle on a number line?

• With a filled circle

• With a square

• With an open circle

• With a dashed line

What is the purpose of choosing a test point in solving inequalities?

• To simplify the inequality

• To eliminate incorrect solutions

• To determine where to shade on the number line

• To find the exact solution

How do you determine where to shade on a number line for inequalities?

• By solving the equation

• By using test points

• By guessing

• By using a calculator

What does an open circle on a number line signify?

• The value is a critical point

• The value is not included in the solution

• The value is included in the solution

• The value is an asymptote

What is the purpose of using a number line in solving inequalities?

• To simplify the inequality

• To find exact solutions

• To visualize the solution set

• To eliminate incorrect solutions

What is the purpose of using a number line in solving inequalities?

• To simplify the inequality

• To eliminate incorrect solutions

• To visualize the solution set

• To find exact solutions

In the graphical method, what does shading below the graph indicate?

• Values not part of the solution

• Values less than the inequality

• Values equal to the inequality

• Values greater than the inequality