Understanding Derivatives and Trigonometric Functions

The video tutorial explains how to find the derivative of trigonometric functions, specifically focusing on F(x) = 2sin(x) and G(x) = -2cos(x). It demonstrates calculating derivatives at specific points using both reference triangles and the unit circle. The tutorial also includes graphical interpretations of the functions and their tangent lines, emphasizing the concept of slope at a point. Two examples are provided: one for F(x) at π/4 and another for G(x) at 7π/6, illustrating the process of finding and interpreting derivatives.

What is the derivative of f(x) = 2sin(x)?

• 2sin(x)

• -2sin(x)

• 2cos(x)

• -2cos(x)

How can the cosine of π/4 be calculated using a reference triangle?

• 1 divided by 2

• Square root of 2 divided by 2

• 1 divided by square root of 2

• Square root of 3 divided by 2

What is the value of 2cos(π/4)?

• 0

• 2

• Square root of 2

• 1

What is the slope of the tangent line to f(x) = 2sin(x) at x = π/4?

• 0

• 2

• Square root of 2

• 1

What is the derivative of g(x) = -2cos(x)?

• 2cos(x)

• -2cos(x)

• -2sin(x)

• 2sin(x)

What is the sine of 7π/6 on the unit circle?

• -Square root of 3/2

• 1/2

• -1/2

• Square root of 3/2

What is the value of 2sin(7π/6)?

• -1

• 0

• 2

• 1

Which trigonometric identity is used to find the derivative of cosine?

• Derivative of sine is cosine

• Derivative of cosine is negative sine

• Derivative of tangent is secant squared

• Derivative of secant is secant times tangent

What is the slope of the tangent line to g(x) = -2cos(x) at x = 7π/6?

• 1

• 2

• -1

• 0

What does evaluating a derivative function at a specific value of x determine?

• The y-intercept of the function

• The minimum value of the function

• The slope of the tangent line at that point

• The maximum value of the function