Question

Help Please!!!!!!
Use a sum or difference identity to write sin(x-pi/4) as a function of x alone?

Will give medal!!!!!! Please

Answer 1

hmmm so.... what's are the \(\bf sin\left( \cfrac{\pi }{4}\right)\quad and\quad cos\left( \cfrac{\pi }{4}\right)\) anyway?

Answer 2

Sin (pi/4) = sqrt 2/2 and cos (pi/4)= is the same thing

Answer 3

ok... let us use that then

\(\bf sin\left( x- \cfrac{\pi }{4}\right)
\\ \quad \\
sin({\color{brown}{ \alpha}} - {\color{blue}{ \beta}})=sin({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}})- cos({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})\qquad thus
\\ \quad \\
sin(x)\cdot cos\left( \frac{\pi }{4} \right)-cos(x)\cdot sin\left( \frac{\pi }{4} \right)\quad
\begin{cases}
cos\left( \frac{\pi }{4} \right)=\cfrac{\sqrt{2}}{2}\\
sin\left( \frac{\pi }{4} \right)=\cfrac{\sqrt{2}}{2}
\end{cases}\quad thus
\\ \quad \\
sin(x)\cdot \cfrac{\sqrt{2}}{2}-cos(x)\cdot \cfrac{\sqrt{2}}{2}\)

Answer 4

Okay, would you keep going after that?

Answer 5

hmmm missing a - there.. . one sec

Answer 6

\(\bf sin(x)\cdot \cfrac{\sqrt{2}}{2}-cos(x)\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}sin(x)}{2}-\cfrac{\sqrt{2}cos(x)}{2}
\\ \quad \\
\cfrac{\sqrt{2}sin(x)-\sqrt{2}cos(x)}{2}\implies \cfrac{\sqrt{2}[sin(x)-cos(x)]}{2}\)

Answer 7

Alright awesome thank you!!

Answer 8

yw