Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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 your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
