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avatar+81 

Write as an algebraic expression of u.

\(cos(tan^{-1}(u))\)

 Apr 20, 2019
 #1
avatar+104026 
+2

tan-1 (u)   = θ   which implies that

 

tan (θ)  =  u   =  u / 1

 

So.....tan =  y / x     which implies that    y = u   and  x  = 1

 

And   cos ( θ)  =  x / r

 

So    r  = √ [ x^2 +  y^2 ]  =  √[ 1^2 + u^2 ]  = √ [ 1 + u^2 ]

 

So....putting all this together

 

cos ( tan-1 (u) )  =  cos (θ)   =  x / r  =     1 / √ [ 1 + u^2 ]

 

 

cool cool cool

 Apr 20, 2019
 #2
avatar+81 
0

Is there a way to do it using like pythagorean identities and stuff like that? That's the way my professor wants us to do it.

MemeLord  Apr 20, 2019
 #3
avatar+104026 
+2

I thnk that you might mean this????

 

tan-1 ( u)  = θ    means that   tan (θ)  = u  =  u / 1   =  y / x

 

So....by the Pythagorean Theorem.....

 

x^2 + y^2  =  r^2

 

1^2 + u^2  = r^2     take both roots

 

±√[ 1 + u^2 ]  =  r

 

So   cos  θ  =    x / r  =   ±1 / √[ 1 + u^2 ]

 

[ I forgot to take both roots in my first answer ]

 

 

cool cool cool

 Apr 20, 2019
 #4
avatar+81 
+2

Close enough I guess.

MemeLord  Apr 20, 2019

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