Solve the Last Big Question on Degrees: Sin(45ds+x)+cos(45ds+x)=sqrt2cosx

  • Context: Undergrad 
  • Thread starter Thread starter majinknight
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Discussion Overview

The discussion revolves around solving a trigonometric equation involving sine and cosine functions with degrees, specifically the equation Sin(45ds+x) + Cos(45ds+x) = sqrt(2)Cos(x). Participants explore various approaches to manipulate and simplify the equation, seeking assistance in resolving the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how to manipulate the left side of the equation and seeks help in solving it.
  • Another participant suggests that the problem involves trigonometric identities related to special angles and encourages looking at provided resources.
  • A different participant provides the sine and cosine addition formulas, questioning the understanding of the values of sin(45) and cos(45).
  • One participant acknowledges understanding after considering the value of 1/sqrt(2) and expresses gratitude for the help received.
  • Several participants engage in casual conversation about personal details, such as age and location, which diverges from the mathematical discussion.
  • One participant tests mathematical typesetting by rewriting the sine addition formula and simplifying it, showing the relationship between the terms.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the solution to the equation. Participants present various approaches and insights, but there remains uncertainty and differing levels of understanding regarding the problem.

Contextual Notes

Some participants reference specific trigonometric identities and values, but there is no resolution on the mathematical steps needed to solve the equation completely. The conversation also includes informal exchanges unrelated to the mathematical problem.

Who May Find This Useful

Students studying trigonometry, particularly those working on homework problems involving sine and cosine functions, may find this discussion relevant.

majinknight
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Ok the last question on those pages of question is this and i have got stuck and can't figure it out. I need to show that (ds=degrees)
Sin(45ds+x) +cos(45ds+x) = sqaureroot2 cosx.
Ok so i did left side first and changed it to.
Sin45Cosy + Cos45Siny +Cos45Cosy - Sin45Siny
Now what i want to do is divide out the CosY and Sin Y but even if i do that it doesn't make square root two and i don't know what to do from there. Can you help me solve this last practise question.
 
Mathematics news on Phys.org
They've given you a trig problem that includes the sine and cosine of
a special angle. That should prod you in the right direction. If not, look at the attached text file.
 

Attachments

What you are doing doesn't make a whole lot of sense. What is Y?

sin(45+ x)= sin(45)cos(x)+ cos(45)sin(x) and
cos(45+ x)= cos(45)cos(x)- sin(45)sin(x).

Do you know what sin(45) and cos(45) are?

Plug those into the two equations above and add.
 
Oh ok i get it, you i thought of putting the 1/root2 in but wasnt sure how to go from there but i understand now. Thankyou so much!
 
Originally posted by majinknight
Ok the last question on those pages of question is this and i have got stuck and can't figure it out. I need to show that (ds=degrees)
Sin(45ds+x) +cos(45ds+x) = sqaureroot2 cosx.
Ok so i did left side first and changed it to.
Sin45Cosy + Cos45Siny +Cos45Cosy - Sin45Siny
Now what i want to do is divide out the CosY and Sin Y but even if i do that it doesn't make square root two and i don't know what to do from there. Can you help me solve this last practise question.


how old are you buddy?
 
16 currently in grade 11. Why?
 


Originally posted by PrudensOptimus
how old are you buddy?

Haven't you discovered the "Profile" button yet, buddy? :)
 
Just testing out the "math typesetting" thing:

<br /> \begin{align*}<br /> \sin(45^\circ + x) &amp;= \sin(45^\circ) \cos x + \cos(45^\circ) \sin x \\<br /> &amp;= \frac{\cos x}{\sqrt{2}} + \frac{\sin x}{\sqrt{2}} \\<br /> &amp;= \frac{\cos x + \sin x}{\sqrt{2}}<br /> \end{align*}<br />
 
Originally posted by majinknight
16 currently in grade 11. Why?


lol which state are you in?
 
  • #10
Im in Ontario Canada. Its a province not a state.
 
  • #11
are you in the Canadian school system?
 
  • #12
Yes i am, i am glad you are all so interested in me. I feel so special :wink:
 
  • #13
heh, it sounded a lot like one of our A-level questions, i was curious about it. :wink:
 

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