Trigonometric Functions and Their Periods

The video tutorial from We Academy discusses how to find the periods of various trigonometric functions. It covers examples including cos(3x + 5 + 7), tan(5x), |sin(x)|, and a complex tan function. The tutorial explains the formulas and steps needed to calculate the periods, emphasizing the importance of understanding trigonometric properties. The video concludes with a call to action to like and subscribe.

What is the main topic discussed in the video?

• Integrals of trigonometric functions

• Trigonometric identities

• Periods of trigonometric functions

• Derivatives of trigonometric functions

What is the formula for finding the period of cos(ax + b)?

• a/π

• a/2π

• π/a

• 2π/a

What is the period of the function cos(3x + 5) + 7?

• π

• 2π/3

• π/3

• 2π

What is the formula for finding the period of tan(ax)?

• a/2π

• a/π

• 2π/a

• π/a

What is the period of the function tan(5x)?

• 5/π

• π/5

• π

• 5π

What is the period of |sin(x)|?

• π/2

• 3π

• π

• 2π

What trigonometric identity is used to find the period of |sin(x)|?

• sin(180° + θ) = -sin(θ)

• tan(180° + θ) = tan(θ)

• sin(90° + θ) = cos(θ)

• cos(90° + θ) = -sin(θ)

What is the general form of the function discussed in the section on tan(x + 4x + 9x + ... + n²x)?

• tan(dx)

• tan(cx)

• tan(bx)

• tan(ax)

What is the formula for the sum of squares of numbers?

• n(n + 1)/2

• n(n + 1)(2n + 1)/6

• n(n - 1)(2n - 1)/6

• n(n - 1)/2

What is the period of the function tan(x + 4x + 9x + ... + n²x)?

• 6π/(n(n + 1)(2n + 1))

• π/(n(n + 1)(2n + 1))

• 3π/(n(n + 1)(2n + 1))

• 2π/(n(n + 1)(2n + 1))