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aniked [119]
1 year ago
14

Write the equation of the trigonometric graph.

Mathematics
1 answer:
prisoha [69]1 year ago
6 0

Answer:

f(x)= \sin(6x)+3

Step-by-step explanation:

The parent function of this graph is:  y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

f(x) = \sf A \sin (B(x + C)) + D

  • A = amplitude (height from the mid-line to the peak)
  • 2π/B = period (horizontal distance between consecutive peaks)
  • C = phase shift (horizontal shift - positive is to the left)
  • D = vertical shift

The parent function y = sin(x) has the following:

  • Amplitude (A) = 1
  • Period = 2π
  • Phase shift (C) = 0
  • Vertical shift (D) = 0
  • Mid-line:  y = 0

From inspection of the given graph:

  • Amplitude (A) = 1
  • \sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}
  • Phase shift (C) = 0
  • Vertical shift (D) = +3  (as mid-line is y = 3)

\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6

Substituting the values into the standard form:

\implies f(x) =1 \sin (6(x + 0)) + 3

\implies f(x) = \sin (6x) + 3

Therefore, the equation of the given trigonometric graph is:

f(x)= \sin(6x)+3

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Complete Question

Answer:

a

  SE  = 0.66}

b

-3.29 <  \mu_1 - \mu_2 <  -0.70  

Step-by-step explanation:

From the question we are told that

  The sample size is  n  = 60

   The first sample mean is  \= x _1  =  8

    The second sample mean is   \= x _2  =  10

    The first variance is  v_1 =  0.25

    The first variance is  v_2 =  0.55

Given that  the confidence level is 95% then the level of significance is 5% =  0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the first standard deviation is  

     \sigma_1 =  \sqrt{v_1}

=>   \sigma_1 =  \sqrt{0.25}

=>   \sigma_1 =  0.5

Generally the second standard deviation is

     \sigma_2 =  \sqrt{v_2}

=>   \sigma_2 =  \sqrt{0.55}

=>   \sigma_2 =  0.742    

Generally the first standard error is

     SE_1  =  \frac{\sigma_1}{\sqrt{n} }

      SE_1  =  \frac{0.5}{\sqrt{60} }

     SE_1  =  0.06

Generally the second standard error is

     SE_2  =  \frac{\sigma_2}{\sqrt{n} }

      SE_2  =  \frac{0.742}{\sqrt{60} }

     SE_2  =  0.09

Generally the standard error of the difference between their mean scores is mathematically represented as    

      SE  =  \sqrt{SE_1^2 + SE_2^2 }

=>     SE  =  \sqrt{0.06^2 +0.09^2 }

=>     SE  = 0.66}

Generally 95% confidence interval is mathematically represented as  

      (\= x_1 -\= x_2) -(Z_{\frac{\alpha }{2} } *  SE) <  \mu_1 - \mu_2 <  (\= x_1 -\= x_2) +(Z_{\frac{\alpha }{2} } *  SE)

=> (8 -10) -(1.96 *  0.66) <  \mu_1 - \mu_2 <  (8-10) +(Z_{\frac{\alpha }{2} } *  0.66)  

=>  -3.29 <  \mu_1 - \mu_2 <  -0.70  

 

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