SOLUTION: I have a verbal exam question that confuses me.
How would I prove that sin(x + Pi/2)=cos(x) and cos(pi/2)=-sin(x) and then use these proofs to prove that (cos(x))'=-sin(x), if w
Algebra.Com
Question 1194018: I have a verbal exam question that confuses me.
How would I prove that sin(x + Pi/2)=cos(x) and cos(pi/2)=-sin(x) and then use these proofs to prove that (cos(x))'=-sin(x), if we assume that (sin(x))'=cos(x)?
I am at loss regarding how I should create this collected explanation.
I would love any help sent my way.
Kind regards
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
You misstated your problem: You want to prove \ =\ -\sin(x))
Use the addition formulas:
\ =\ \sin(\alpha)\cos(\beta)\ +\ \cos(\alpha)\sin(\beta))
\ =\ \cos(\alpha)\cos(\beta)\ -\ \sin(\alpha)\sin(\beta))
To prove both \ =\ \cos(x))
and
Then \ =\ \frac{d}{dx}\,\sin\(x\,+\,\frac{\pi}{2}\))
Use the chain rule: Let 
\ =\ \cos(u))
from the assumption, then
\ =\ \cos\(x\,+\,\frac{\pi}{2}\)\ =\ -\sin(x))
John
My calculator said it, I believe it, that settles it
From
I > Ø
RELATED QUESTIONS
prove... (answered by lwsshak3)
how do i verify and prove that
sin(beta - 3[pi]/2) = cos... (answered by lwsshak3)
Given that cos x = 3/5 and sin x is positive.
What is sin (x -pi), cos (x- pi), sin... (answered by rothauserc)
"compute the exact values of sin 2x, cos 2x, tan 2x without a calculator. Cos x= (-4/5),... (answered by Edwin McCravy)
could you please help me find sin(2x) and cos(2x)
sinx= 3/√10 and pi/2 < x < pi
(answered by Alan3354,rothauserc)
hey, i am doing a exam review packet for my math class. i am having a ton of problems... (answered by user_dude2008)
Hey, Tutor
Thanks for taking the time to help me. I have a few questions about graphing... (answered by ikleyn)
prove 2cot2xcosx=cscx-2sinx
I tried starting on the left. My work is... (answered by addingup)
prove that... (answered by lwsshak3)