Trigonometric Functions and Their Properties

The video tutorial explains how to solve the trigonometric equation sine x = cosine x over a given interval using three different methods: algebraic manipulation with tangent substitution, the unit circle approach, and graphical analysis. Each method is explored in detail, demonstrating how to find angles where the tangent function equals +1, and confirming solutions using reference angles and the unit circle. The tutorial concludes by graphing sine and cosine functions to visually identify points of intersection, reinforcing the solutions found algebraically and geometrically.

What is the first step in solving the equation sine x = cosine x algebraically?

• Add cosine x to both sides

• Divide both sides by cosine x

• Subtract sine x from both sides

• Multiply both sides by sine x

What is the tangent of 45 degrees?

• Undefined

• -1

• 1

• 0

In which quadrant are both x and y coordinates negative, making tangent positive?

• Second quadrant

• First quadrant

• Third quadrant

• Fourth quadrant

What is the angle in radians for 225 degrees?

• 3π/4

• 2π

• 5π/4

• π/2

On the unit circle, when are sine and cosine equal?

• When the angle is π/4

• When the angle is 3π/4

• When the angle is π

• When the angle is π/2

Which method involves finding where the y-coordinate equals the x-coordinate?

• Algebraic method

• Reference angle method

• Unit circle method

• Graphical method

Which angle in radians corresponds to the second solution found using the unit circle?

• 3π/4

• π/4

• 5π/4

• 7π/4

What is the x-coordinate of the intersection point of y = sine x and y = cosine x?

• π

• 3π/4

• π/2

• π/4

What is the significance of the intersection points in the graphical method?

• They represent the points where sine is zero

• They represent the minimum values

• They represent the points where sine and cosine are equal

• They represent the maximum values

What is the main advantage of using multiple methods to solve the equation?

• It is easier

• It is more accurate

• It provides a deeper understanding

• It is faster