A community for students.
Here's the question you clicked on:
 0 viewing
UnkleRhaukus
 3 years ago
\[f(x)=3\sin(x)2\cos(x)\]
UnkleRhaukus
 3 years ago
\[f(x)=3\sin(x)2\cos(x)\]

This Question is Closed

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0\[\begin{align*} f(x)&=3\sin(x)2\cos(x)\\ &=\sqrt{(2)^2+3^2}\cos\Big(x\text{arctan2}\big({3,2}\big)\Big)\\ &=\sqrt{13}\cos\Big(x\big(\pi+\arctan(\tfrac3{2})\big)\Big)\\ &=\sqrt{13}\cos\left(x\pi+\arctan(\tfrac3{2})\right)\\ &=\sqrt{13}\sin\big(x\tfrac\pi2+\arctan(\tfrac3{2})\big)\\ &\approx\sqrt{13}\sin\big(x0.588\big)\\ \\ &A=\sqrt{13}\\ &\phi=\frac\pi2+\arctan(\tfrac3{2})\approx 0.588\\ &T=2\pi\qquad\qquad\omega=\tfrac1{2\pi}\\ \end{align*}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's\[f(x)=\sqrt{3^2+(2)^2}\sin \left( x\arctan \left( \frac{ 2 }{ 3 } \right) \right)\]\[\approx \sqrt{13}\sin (x 0.588)\]So you are right, but you made a typo in the equation editor (3/2 instead of 2/3)

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0i can't see the typo

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You wrote\[\arctan \left( \frac{ 3 }{ 2 } \right)\]It must be:\[\arctan \left( \frac{ 2 }{ 3 } \right)\]

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0i have applied these definitions, what method are you using

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I applied the same rule. Your answer is right. You just made a typo in your explanation above (in the equation editor). Just carefully look what you typed there (3/2). In your actual calculation you used 2/3, which is right....

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0i dont think i have made a mistake

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0If 3/2 was the same as 2/3 you didn't ;)

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0\[\tfrac\pi2+\arctan(\tfrac32)\approx 0.588\] \[\qquad\quad\arctan(\tfrac23)\approx 0.588\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.