Does the function y = 3sin (π / 3 + π / 4) have periods and amplitudes?

Yes. The period of a constant function is a non-zero real number. There is no minimum positive period
The amplitude is 0

Find a period of the function y = 3sin (π / 6-3x),

T = 2 π / | w | where | w | = 3, so t = 2 π / 3

Find the minimum positive period of the function y = 3sin (3x + 45 °) cos (3x + 45 °)

y=3sin(3x+45°)cos(3x+45°)
=3/2sin(6x+90°)
=3/2cos6x
Positive period = 3 π / 6 π

How to draw the image of piecewise function in senior one mathematics?

Define the domain
Draw according to the value of the definition field
For example, when x is less than 5, the function y = x + 4
When the function is greater than or equal to 5, the function is y = X-6,
Just draw these two separately~

Given the sinusoidal function y = 3 / 2Sin (1 / 2x + π / 4), the amplitude, period, frequency and initial phase of the function are calculated, and the image of it in a period is made

Amplitude: 3 / 2
Period = 2 π / (1 / 2) = 4 π
Frequency: 1 / 4 π
Primary phase: π / 4
To draw a picture in a period, use the legendary five point method
Let 1 / 2x + π / 4 = 0 solve x = - π / 2, which is the starting point in this period
To find the end point, add the period to the starting point, which is 7 π / 2
Then draw the midpoint 1 between the starting point and the end point, where 1 = (start + end) / 2, and calculate 3 π / 2
Then find out the midpoint 2 between the starting point and the midpoint 1, where the middle 2 = (start + middle 1) / 2, and get π / 2. At this time, the corresponding y is the amplitude of this function 3 / 2
Then find the middle point 3 between the middle 1 and the end point, where the middle 3 = (middle 1 + terminal) / 2, and get 5 π / 2. At this time, the corresponding y is - 3 / 2
Finally, connect the five points and you're done

What is the relationship between the image of function y = 2 / 3sin (x / 2 - π / 4) and sine curve?

SiNx decreases by half to SiNx / 2, shifts Π / 2 to the right, and moves up 2 / 3 as a whole

The period of the function y = 3cosx (π / 3-2x) is amplitude, phase, initial phase and frequency

If the title is correct, then I am responsible to tell you that this function is not a periodic function

Given the function y = 1 / 2Sin (2x + π / 6) + 1, find the amplitude, period, frequency and phase of the function The known function y = 1 / 2 times sin (2x + π / 6) + 1 1. Find the amplitude, period, frequency, phase and initial phase of the function 2. Find the increasing interval, axis and center of symmetry 3. Draw the image of the function y = f (x) on the interval [0, π]

(1) The image of F (x) = asin (Wx + &)
Amplitude a period 2pi / W frequency w / (2pi) phase Wx + & initial phase&
So for this problem, amplitude 1 / 2, period PI, frequency 1 / PI, phase 2x + pi / 6, initial phase pi / 6
(2) Using the relevant principles, we are familiar with the increasing interval of y = SiNx image is [2kpi pi / 2,2kpi + pi / 2], symmetry axis X = KPI + pi / 2, symmetry center (KPI, 0)
In this question, 2kpi pi / 2 = < 2x + pi / 6 = < 2kpi + pi / 2
2x+pi/6=kpi+pi/2
kpi=2x+pi/6
The solution of X range [KPI pi / 3, KPI + pi / 6], x = KPI / 2 + pi / 6, (KPI / 2-pi / 12,0)
So the monotone increasing interval [KPI pi / 3, KPI + pi / 6], axis of symmetry x = KPI / 2 + pi / 6, center of symmetry (KPI / 2-pi / 12,0)
K belongs to Z
（3）
Don't draw the picture. You can draw it yourself

Find the amplitude, minimum positive period, phase and monotone interval of the function y = 1 / 2Sin (2x + π / 4)

Amplitude 1 / 2
Minimum positive period π
Phase: 2x + π / 4
Monotone interval: - π / 2 + 2K π
x∈[-π/4+kπ,π/4+kπ],k∈Z

The definition domain of the function y = 1 / 5sin (3x - π / 3) is, the range of value is, the period is, the amplitude is, the frequency is and the initial phase is The definition domain of the function y = 1 / 5sin (3x - π / 3) is__ , the value range is The period is The amplitude is The frequency is It was_ .

The definition domain of the function y = 1 / 5sin (3x - π / 3) is (- ∞, ∞), the range is [- 1 / 5,1 / 5], the period is 2K π / 3, the amplitude is 1 / 5, the frequency is 3 / 2 π, and the initial phase is - 3 / π

Does the function y = 3sin (π / 3 + π / 4) have periods and amplitudes?