The video tutorial covers the importance of graphing trigonometric functions, particularly in the context of simple harmonic motion. It explains how to handle domain and range variations, graph cosine functions with amplitude and vertical shifts, and confirm graph accuracy using different methods. The tutorial also provides steps to find x-intercepts using inverse cosine and a calculator.

Why is graphing trigonometric functions particularly important in the study of simple harmonic motion?

• It helps in understanding the motion of objects.

• It is only used in theoretical physics.

• It is a prerequisite for calculus.

• It simplifies algebraic equations.

What is a common domain for graphing trigonometric functions in exams?

• 0 to 2π

• -π to π

• 0 to 4π

• -2π to 2π

How does the coefficient '3' affect the graph of y = 3 cos(x)?

• It changes the amplitude.

• It shifts the graph horizontally.

• It changes the period.

• It reflects the graph over the x-axis.

What is the effect of a '-2' in the equation y = 3 cos(x) - 2?

• It changes the amplitude.

• It shifts the graph downwards by 2 units.

• It reflects the graph over the y-axis.

• It shifts the graph upwards by 2 units.

Why is it important to draw graphs large enough when graphing trigonometric functions?

• To avoid making mistakes in calculations.

• To make the graph look impressive.

• To use more paper.

• To accurately depict the features of the graph.

What is the range of the function y = 3 cos(x) - 2?

• From 0 to 2

• From -5 to 1

• From -3 to 3

• From -1 to 1

How can you confirm the accuracy of a trigonometric graph?

• By using a ruler.

• By drawing it multiple times.

• By checking it from different angles.

• By asking a friend.

What operation is used to find x-intercepts in a trigonometric function?

• Differentiate the function.

• Set x to zero.

• Set y to zero.

• Integrate the function.

What is the approximate value of 2π in radians?

• 6.28

• 3.14

• 9.42

• 1.57

Which function is used to find the angle for cos(x) = 2/3?

• Inverse secant

• Inverse cosine

• Inverse tangent

• Inverse sine