Question

Trig question -- please help if you can!

I have to write y = r cos(θ + R) and z = r sin(θ + R) in terms of y, z, and R. I'm not really sure how to do this, so would you mind showing work so I can learn the steps properly? (teacher hasn't taught this super well, haha) Thank you!!

Answer 1

`\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta) \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ y=r[cos(\theta +R)]\implies y=r[cos(\theta )cos(R)-sin(\theta )sin(R)] \\\\\\ y=rcos(\theta )cos(R)-rsin(\theta )sin(R) \\\\\\ z=r[sin(\theta +R)]\implies y=r[sin(\theta )cos(R)+cos(\theta )sin(R)] \\\\\\ z=rsin(\theta )cos(R)+rcos(\theta )sin(R)`