Differentiation and Trigonometric Functions

The video tutorial explores the differentiation of trigonometric functions, focusing on sine, cosine, and tangent. It begins with an introduction to the sine graph and its gradient, followed by plotting the gradient of the sine function. The tutorial then examines changes in the gradient across the sine graph and differentiates sine and cosine functions. The exploration continues with the gradient of the cosine function and concludes with using the quotient rule to differentiate the tangent function.

What is the gradient of the sine function at x = 0?

• Undefined

• -1

• 1

• 0

When x = π/2, what is the gradient of the sine function?

• Undefined

• -1

• 1

• 0

What is the gradient of the sine function at x = π?

• 1

• -1

• Undefined

• 0

What is the derivative of sin(x)?

• -cos(x)

• sin(x)

• cos(x)

• -sin(x)

Which trigonometric function is the derivative of cos(x)?

• -cos(x)

• sin(x)

• cos(x)

• -sin(x)

What is the derivative of tan(x) in terms of sine and cosine?

• sec^2(x)

• cos^2(x)

• csc^2(x)

• sin^2(x)

What rule is used to differentiate a function that is a fraction of two other functions?

• Chain Rule

• Quotient Rule

• Product Rule

• Power Rule

What is the reciprocal function of cos(x)?

• cot(x)

• sec(x)

• csc(x)

• tan(x)

What is the Pythagorean identity involving sine and cosine?

• sin(x) + cos(x) = 1

• sin^2(x) + cos^2(x) = 1

• sin(x) - cos(x) = 1

• sin^2(x) - cos^2(x) = 1

What is the derivative of -sin(x)?

• -sin(x)

• cos(x)

• -cos(x)

• sin(x)