Trigonometric Functions and Graphs

The video tutorial covers trigonometric graphs, focusing on the functions f(x) = 0.5cos(x) and g(x) = sin(x-30). It explains amplitude changes, horizontal shifts, and how to calculate the range of transformed functions. The session also discusses special angles and values, and how to determine when the product of two functions is greater than zero. Finally, it covers gradients and how to identify increasing functions.

What is the main focus of the session?

• Algebraic equations

• Trigonometric graphs

• Statistics

• Calculus

What transformation is applied to the graph of g(x) = sin(x - 30)?

• Horizontal shift to the left

• Reflection

• Vertical shift

• Horizontal shift to the right

How is the length of segment AB determined?

• By adding f(x) and g(x)

• By dividing f(x) by g(x)

• By subtracting g(x) from f(x)

• By multiplying f(x) and g(x)

What is the range of the function 3f(x) + 2?

• [-1, 1]

• [-0.5, 0.5]

• [0, 3]

• [0.5, 3.5]

At what value of x does g(x) - f(x) equal √3/2?

• 30 degrees

• 60 degrees

• 90 degrees

• 120 degrees

In which interval is the product of f(x) and g(x) greater than zero?

• [-90, 0]

• [30, 90]

• [210, 240]

• [90, 150]

Where is the gradient of the shifted graph of g(x) greater than zero?

• [180, 240]

• [120, 180]

• [65, 125]

• [-60, 60]