Derivatives and Trigonometric Functions

This video tutorial covers the derivatives of sine and cosine functions. It begins with an introduction to the concept of derivatives, followed by a proof of the derivative of sine using the limit definition. The video then provides a graphical representation of the derivatives of sine and cosine functions. It proceeds to apply derivative formulas to solve various problems, including an advanced problem involving horizontal tangents. The tutorial aims to enhance understanding of derivatives through both theoretical and practical approaches.

What is the derivative of sine x?

• secant x

• cosine x

• negative sine x

• tangent x

What is the derivative of cosine x?

• tangent x

• negative sine x

• negative cosine x

• sine x

In the proof of the derivative of sine, what is the limit of sine h divided by h as h approaches zero?

• One

• Zero

• Negative one

• Infinity

Graphically, what does the derivative of the sine function represent?

• A constant function

• The cosine function

• The tangent function

• The original sine function

How is the derivative of the cosine function graphically represented?

• As the tangent function

• As the original cosine function

• As a reflection of the sine function across the x-axis

• As a constant function

What is the derivative of x cubed using the power rule?

• 3x squared

• x squared

• x cubed

• 3x

When simplifying the derivative of a function, what should you be cautious about?

• The variables

• The coefficients

• The signs of the terms

• The exponents

What is the derivative of x to the power of -1?

• -1/x squared

• x squared

• 1/x

• -x

What is the sine function value for a 60-degree angle?

• 1

• Square root 2/2

• Square root 3/2

• 1/2

In which quadrants is the sine function positive?

• First and fourth

• Third and fourth

• Second and third

• First and second