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tatuchka [14]
3 years ago
8

What is the value of x? Enter your answer in the box. x =

Mathematics
1 answer:
Alex777 [14]3 years ago
3 0
<h2><u>Solution:</u> </h2>

<u>Steps of Statement: </u>We will solve right Angled ∆ RST. We will use Trigonometric Ratio to solve this Question.

<u>Now, In ∆ RST , Where angle C is 90° and angle D is 60° </u>

∠RTS = 60°

So, Sin 60° = RS / RT

☛ √3/2 = 2√3 / RT

☛ RT = 4

<u>Now, Let's Solve Right angled ∆ QRT </u>

tan 45° = QR / RT

☛ 1 = x / 4

☛ x = 4

<h2>Therefore, Required Value of x is <u>4</u>. </h2>

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Step-by-step explanation:

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Write the equation of the trigonometric graph.
prisoha [69]

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
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  • 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:

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1 year ago
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