Find a possible solution to the equation sin(3x+13)=cos(4x)
1 answer:
Recall that sine and cosine are co-functions. That means they satisfy the equation
For example, sin 30° = cos 60°. Now, using this property, we have
![\sin(3x + 13) = \cos[90 - (3x + 13)]](https://tex.z-dn.net/?f=%5Csin%283x%20%2B%2013%29%20%3D%20%5Ccos%5B90%20-%20%283x%20%2B%2013%29%5D)
As can be seen from the equation provided, it shows that sin(3x + 13) = cos(4x). This means that the left-hand side of the equations are equivalent. Thus, we have
90 - (3x + 13) = 4x
90 - 3x - 13 = 4x
77 = 7x
x = 11
We now have the value of x. We can also check if we got the right answer by substituting the value into the original equation.
Answer: 11
For example, sin 30° = cos 60°. Now, using this property, we have
As can be seen from the equation provided, it shows that sin(3x + 13) = cos(4x). This means that the left-hand side of the equations are equivalent. Thus, we have
90 - (3x + 13) = 4x
90 - 3x - 13 = 4x
77 = 7x
x = 11
We now have the value of x. We can also check if we got the right answer by substituting the value into the original equation.
Answer: 11
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The <em>first three</em> elements of the <em>recursive</em> series are 6, 10, 8. (Correct choice: B)
<h3>How to generate values from a recursive function</h3>
In this question we have a kind of <em>recursive</em> function known as Fibonacci's function, where a value of the series is generated from at least <em>immediately previous</em> elements. In this case, we need to find the <em>first</em> three elements from the <em>fifth</em> and <em>fourth</em> elements of the series:
a₄ = a₅ - a₆ + 4
a₄ = - 2 - 0 + 4
a₄ = 2
a₃ = a₄ - a₅ + 4
a₃ = 2 - (- 2) + 4
a₃ = 8
a₂ = a₃ - a₄ + 4
a₂ = 8 - 2 + 4
a₂ = 10
a₁ = a₂ - a₃ + 4
a₁ = 10 - 8 + 4
a₁ = 6
The <em>first three</em> elements of the <em>recursive</em> series are 6, 10, 8. (Correct choice: B)
To learn more on recursive series: brainly.com/question/8972906
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