Understanding the Intersection of Sine and Cosine Graphs

The video tutorial explores the intersection points of the graphs of y = sin(θ) and y = cos(θ) within the range of 0 to 2π. It begins by setting up the unit circle and explaining the coordinates for sine and cosine. The tutorial then graphs both functions, identifying key points and visually determining the intersection points. Finally, it calculates the exact values of these intersection points using geometric principles, specifically focusing on angles like π/4 and 5π/4.

What is the main objective of the problem discussed in the video?

• To calculate the derivative of sine and cosine functions.

• To determine the points where the graphs of y = sin(θ) and y = cos(θ) intersect.

• To find the area under the sine and cosine curves.

• To find the maximum value of sine and cosine functions.

What is the value of cos(θ) when θ is 0?

• Undefined

• 1

• -1

• 0

At which angle is sin(θ) equal to 1?

• π

• π/2

• 3π/2

• 0

What is the value of sin(θ) at θ = π?

• 1

• 0

• -1

• Undefined

How many points of intersection are there between the graphs of y = sin(θ) and y = cos(θ) in the interval [0, 2π]?

• 1

• 2

• 3

• 4

Which angle corresponds to the first intersection point of y = sin(θ) and y = cos(θ)?

• π

• 3π/4

• π/2

• π/4

What is the x-coordinate of the intersection point at θ = π/4?

• 1

• -√2/2

• 0

• √2/2

What is the y-coordinate of the intersection point at θ = 5π/4?

• -√2/2

• 0

• 1

• √2/2

What is the reference angle for θ = 5π/4?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

What is the value of both sin(θ) and cos(θ) at the intersection point θ = 5π/4?

• √2/2

• -√2/2

• 0

• 1