Trigonometric Functions Transformations

This video by Mr. Arnold on Hegerty Maths covers transformations of trigonometric graphs, focusing on translations and stretches. It explains how adding a constant to a function translates it vertically, while adding to the input translates it horizontally. The video also covers vertical and horizontal stretches, detailing how they affect the periodicity and amplitude of trig functions. The tutorial is aimed at A-level maths students but is applicable to other math modules.

What is the main focus of the video presented by Mr. Arnold?

• Solving algebraic equations

• Transformations of trigonometric graphs

• Statistics and probability

• Calculus and its applications

What happens to the graph of y = cos(x) when a constant is added to it?

• It stretches vertically

• It compresses horizontally

• It shifts horizontally

• It shifts vertically

In the function y = 1 + cos(x), what is the new maximum value of the graph?

• 0

• 1

• 2

• 3

What is the effect of adding a constant to the x variable in a trigonometric function?

• Vertical stretch

• Horizontal stretch

• Horizontal translation

• Vertical translation

Where does the asymptote of y = tan(x + 90) shift to from 270 degrees?

• 180 degrees

• 360 degrees

• 90 degrees

• 0 degrees

What is the period of the function y = tan(x)?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

What is the effect of multiplying a trigonometric function by a constant?

• Horizontal stretch

• Vertical stretch

• Vertical translation

• Horizontal translation

For the function y = 2cos(x), what is the new range of the graph?

• 0 to 1

• -1 to 1

• -2 to 2

• -3 to 3

What is the period of the function y = cos(x)?

• 180 degrees

• 270 degrees

• 360 degrees

• 90 degrees

What is the effect of a vertical stretch on the amplitude of a trigonometric function?

• No effect on the amplitude

• Decreases the amplitude

• Increases the amplitude

• Reverses the amplitude