In general, in y=asin[k(x-d)]+c the equation of the axis of the curve  is determined by the value of

Question 12 options:

a)

a

b)

c

c)

d

d)

k

In the equation \( y = a \sin[k(x - d)] + c \), the equation of the axis of the curve is determined by the value of \( c \).

The value \( c \) represents the vertical translation of the sine curve, shifting the entire graph up or down by \( c \) units. This translation changes the horizontal axis (or midline) of the sine function, which is the average value around which the sine wave oscillates.

So, the correct answer is:

b) \( c \)

Would you like more details or have any questions?

Here are 5 more questions you might want to ask:

1. How does the amplitude of the sine function change with the value of \( a \)?
2. What is the effect of the value of \( k \) on the period of the sine function?
3. How do you find the phase shift in the equation \( y = a \sin[k(x - d)] + c \)?
4. What are some real-life applications of sine and cosine functions?
5. How does the graph of \( y = \cos(x) \) differ from \( y = \sin(x) \)?

**Tip:** Understanding the transformations of trigonometric functions can greatly help in sketching their graphs and analyzing their properties.

Explore how the axis of a sine curve is determined by the value of 'c' in the equation y = a sin[k(x - d)] + c. This concept is crucial in trigonometry, affecting the vertical translation of the sine function and its midline. Ideal for students in Grades 11-12 studying advanced trigonometric functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation