Sine Functions and Their Properties

The video tutorial explains how to solve equations using graphs, focusing on sine functions. It covers visualizing graphs, finding intersections, and understanding periodicity. The tutorial also discusses the use of calculators for approximations and highlights the concept of multiple solutions due to the periodic nature of sine functions.

What is the range of values that the sine function can take?

• 0 to 1

• -1 to 1

• -2 to 2

• 0 to 2

What is the significance of the intersection points of two graphs?

• They show where the graphs have the same slope.

• They represent the points where the graphs are equal.

• They mark the maximum values of the graphs.

• They indicate where the graphs are parallel.

How often does the sine graph repeat itself?

• Every 90 degrees

• Every 180 degrees

• Every 360 degrees

• Every 270 degrees

Why does a calculator only provide the first solution for a sine equation?

• It cannot compute more than one solution.

• It shows the solution with the highest value.

• It is programmed to show only the smallest solution.

• It provides the first solution due to the infinite nature of solutions.

What is the term for angles between 0 and 90 degrees?

• Acute

• Right

• Obtuse

• Reflex

If a sine equation has a solution of 30 degrees, what is another possible solution within 0 to 360 degrees?

• 60 degrees

• 150 degrees

• 90 degrees

• 210 degrees

What is the first step in solving a sine equation using a calculator?

• Find the cosine of the angle.

• Multiply the angle by 2.

• Use the sine inverse function.

• Subtract 90 degrees from the angle.

When solving sine equations, why might you need to approximate the solution?

• Because the sine function is not defined for all angles.

• Because the exact value is always zero.

• Because the calculator cannot handle decimals.

• Because the solution might not be a neat number.

What is the next step after finding the first solution to a sine equation?

• Divide the solution by 2.

• Multiply the solution by 2.

• Subtract the solution from 180 degrees.

• Add 90 degrees to the solution.

What should you do if your calculator gives a solution that seems incorrect?

• Check the solution by calculating the sine of the angle.

• Assume the solution is correct and move on.

• Ignore the solution and try again.

• Use a different calculator.