Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Which values represent solutions to cosine (startfraction pi over 4 endfraction minus x) = startfraction startroot 2 endroot over 2 endfraction sine x, where x is an element of [0, 2pi)?

Sagot :

The given trigonometric function consists of trigonometric values of common angles.

The values that represent the solution to [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex], x ∈ [0, 2·π) are; [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].

What are trigonometric functions?

  • Trigonometric functions are real functions in mathematics that connect an angle of a right-angled triangle to ratios of two side lengths.
  • They are widely utilized in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.

The given function is:  [tex]cos(\frac{\pi }{4} -x)=\frac{\sqrt{2} }{2} .sinx[/tex]

Where; x ∈ [0, 2·π).

We have; cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B).

  • [tex]cos(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}, sin(\frac{\pi }{4} )=\frac{\sqrt{2} }{2}[/tex]

Which gives:

  • [tex]cos(\frac{\pi }{4}-x )=\frac{\sqrt{2} }{2}. cosx+\frac{\sqrt{2} }{2}.sinx[/tex]

So, we obtain:
[tex]\frac{\sqrt{2} }{2} .cosx=\frac{\sqrt{2} }{2}.sinx-\frac{\sqrt{2} }{2} .sinx=0\\cosx=0\\cos\frac{\pi }{2} =0[/tex]

Therefore, the possible solutions (x-values) to cos x = 0 are:

[tex]0[/tex] ≤ [tex]\frac{n.\pi }{2}[/tex] ≤ [tex]2.\pi[/tex]

Where, n = 1, 3, 5, .., x ∈ [0, 2·π)

We get:  [tex]x=({\frac{\pi }{2} or \frac{3.\pi }{2} )[/tex].

Know more about trignometric funcions here:

https://brainly.com/question/24349828

#SPJ4

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.