A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
cos(2tan1(x))
anonymous
 5 years ago
cos(2tan1(x))

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its arctan, the 1 is suppose to be a ^1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0must use \[cos(2\theta)=cos^2(\theta)sin^2(\theta)\] so you need \[cos(tan^{1}(x))\] and \[sin(tan^{1}(x))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know how to find them?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok do this { draw a right triangle and label one angle as theta, theta =\[tan^{1}(x)\] the angle whose tangent is x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0since tangent is \[\frac{opp}{adj}\] label the opposite angle x and the adjacent angle as 1 so you have \[\frac{x}{1}=x\] as the tangent of your angle

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0by pythagoras the hypotenuse is\[\sqrt{x^2+1}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[sin(tan^{1}(x))=\frac{opp}{hyp}=\frac{x}{\sqrt{x^2+1}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[cos(tan^{1}(x))=\frac{adj}{hyp}=\frac{1}{\sqrt{x^2+1}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now use the "double angle" formula to find \[cos(2tan^{1}(x))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is the top line i wrote. calling \[tan^{1}(x)=\theta\] it is \[cos^2(\theta)sin^2(\theta)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you get \[\frac{1}{x^2+1}\frac{x^2}{x^2+1}=\frac{1x^2}{x^2+1}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the important part is being able to find \[sin(tan{1}(x))\] or \[sin(tan{1}(x))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i think i made a mistake on the last post where i said \[cos(tan^{1}(x))\] was something else. it is \[\frac{1}{\sqrt{x^2+1}}\]
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.