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

[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.

 

[pnaj]

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.

 

[HallsofIvy]

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.

 

[majinknight]

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!

 

[PrudensOptimus]

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?

 

[majinknight]

16 currently in grade 11. Why?

 

[Muzza]

Originally posted by PrudensOptimus
how old are you buddy?

Haven't you discovered the "Profile" button yet, buddy? :)

 

[Tron3k]

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 />

 

[PrudensOptimus]

Originally posted by majinknight
16 currently in grade 11. Why?

lol which state are you in?

 

[majinknight]

Im in Ontario Canada. Its a province not a state.

 

[jake_at]

are you in the Canadian school system?

 

[majinknight]

Yes i am, i am glad you are all so interested in me. I feel so special

 

[jake_at]

heh, it sounded a lot like one of our A-level questions, i was curious about it.