Sine and Cosine Function Concepts

The video tutorial explores the properties of sine and cosine graphs, focusing on their intercepts and how they combine to form a new graph. It discusses the points of intersection, symmetry, and zero points, highlighting the periodic nature of the resulting graph. The tutorial concludes by explaining the concept of wave functions, emphasizing the changes in amplitude and phase when sine and cosine are combined.

What are the intercepts of the sine function on the x-axis?

• 0, 90, 180

• 90, 270, 360

• 0, 180, 360

• 90, 180, 270

At x = 0, what is the combined height of the sine and cosine graphs?

• 0

• 1

• -1

• 2

What is the value of sin(45) + cos(45)?

• √2

• 2

• 1

• 0.707

At which angle does the graph of y = sin(x) + cos(x) cross the x-axis between 90 and 180 degrees?

• 150 degrees

• 180 degrees

• 135 degrees

• 90 degrees

What is the periodicity of the graph of y = sin(x) + cos(x)?

• 180 degrees

• 270 degrees

• 90 degrees

• 360 degrees

How does the amplitude of y = sin(x) + cos(x) compare to a standard sine wave?

• It is zero

• It is smaller

• It is the same

• It is larger

What is the phase shift of the graph of y = sin(x) + cos(x)?

• Shifted to the left

• Shifted upwards

• Shifted to the right

• No shift

What type of functions are sine and cosine referred to as?

• Linear functions

• Exponential functions

• Quadratic functions

• Wave functions

What is the range of the graph of y = sin(x) + cos(x)?

• -√2 to √2

• 0 to 1

• -2 to 2

• -1 to 1

What is the main characteristic of the graph of y = sin(x) + cos(x) that makes it different from a parabola?

• It is quadratic

• It is periodic

• It is linear

• It is constant