Table of Contents
What transformation affects the period of a sinusoidal function?
There are 5 transformations that can affect trig functions: horizontal stretch (HS) alters the period. vertical stretch (VS) alters the amplitude. horizontal translation (HT) causes a phase shift relocating our initial point.
What is C in trigonometric graphs?
C is for cruisin’ left or right in a trigonometry equation The value of C changes the graph by moving the whole curve to the left or right of where it usually is. If you subtract C, the graph moves C units to the right.
Which transformation affects the period of trigonometric function?
B is for becoming (the period) in a trig equation The multiplier B affects the length of the graph’s period, or how far it goes along the x-axis. The sine, cosine, cosecant, and secant all normally have a period of 2π. The tangent and cotangent have a period of π.
How do you change the period of a sine function?
To get the period of the sine curve for any coefficient b, just divide 2π by the coefficient b to get the new period of the curve. The coefficient b and the period of the sine curve have an inverse relationship, so as b gets smaller, the length of one cycle of the curve gets bigger.
How does changing the value of c affect the graph?
As we can see from the graph, changing c affects the vertical shift of the graph. When c > 0, the graph shifts up c units. When c < 0, the graph shift down c units. In other words, when |a| > 1 (absolute value of a), the graph compresses.
How do you find c on a graph?
The c-value is where the graph intersects the y-axis. In this graph, the c-value is -1, and its vertex is the highest point on the graph known as a maximum. The graph of a parabola that opens up looks like this. The c-value is where the graph intersects the y-axis.
What is a period in trig graphs?
The period is the distance between each repeating wave of the function, so from tip to tip of the function’s graph. As you can see from this graph, the distance between the tips of the function is 3.034 – 1.463 = 1.57.
How to find the period of a trigonometric function with b > 0?
P = 2π / | b | and becomes P = 2π / b for b > 0. Interactive tutorials on Period of trigonometric functions may first be used to understand this concept. The graph below is that of a trigonometric function of the form y = a sin (b x), with b > 0. Find its period and the parameter b.
How do you find the period of a sin function?
Therefore, to find the period of the function f ( x) = A sin ( Bx + C) + D, we follow these steps: Plug B into 2π / | B |. For example, consider the function f ( x) = 3sin (π x + 1) – 7.
What is the period of the Sinin(x + pi/2) = cos x y = cosx?
sin (x + π/2) = cos x y = cos x graph is the graph we get after shifting y = sin x to π/2 units to the left Period of the cosine function is 2π
What is the period of the cosine function on the graph?
y = cos x graph is the graph we get after shifting y = sin x to π/2 units to the left Period of the cosine function is 2π There are a few similarities between the sine and cosine graphs, They are: Both have the same curve which is shifted along the x-axis