Differentiating Trigonometric Functions

The video tutorial covers the application of differentiating trigonometric functions, focusing on finding tangents to curves. It begins with an introduction to the topic, followed by a detailed explanation of using derivatives to find tangents. The instructor demonstrates the use of point-gradient form and applies the chain rule for differentiation. The lesson concludes with a sense check to ensure understanding.

What is the primary focus of the video tutorial?

• Solving algebraic equations

• Applications of differentiating trigonometric functions

• Applications of integrating trigonometric functions

• Graphing linear functions

Which form is most useful for finding the equation of a tangent?

• Vertex form

• Point-gradient form

• Standard form

• Slope-intercept form

What is the value of cos(90 degrees) or cos(pi/2)?

• 1

• 0

• -1

• Undefined

Which rule is used to differentiate the function in the video?

• Product rule

• Quotient rule

• Chain rule

• Power rule

What is the derivative of cos(2x) with respect to x?

• cos(2x)

• -sin(2x)

• 2cos(2x)

• -2sin(2x)

What should you substitute into the gradient function to find the gradient at a specific point?

• The tangent

• The x-coordinate

• The slope

• The y-coordinate

What is the gradient of the tangent line at x = pi/4?

• 0

• 2

• 1

• -2

What is the equation of the tangent line derived in the video?

• y = 2x + pi/2

• y = -2x + pi/2

• y = x - pi/2

• y = -x + pi/2

How does the graph of cos(2x) differ from cos(x)?

• It is stretched vertically

• It is reflected over the x-axis

• It is shifted horizontally

• It is squished horizontally

What is the importance of verifying the solution with a sketch?

• To check for calculation errors

• To ensure the graph is colorful

• To make the graph look symmetrical

• To add labels to the graph