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avatar+86 

If x = arctan(-1/5) and x + y = 290 degrees, then cos y = ?

 

The "answer" that it shows is not a real answer and I'm still in need of one. 

 Apr 19, 2018
edited by SurpriseMe  Apr 20, 2018
 #2
avatar+17338 
+2

                                  arctan(-.2) = 168.69      and     348.69 degrees

x+y = 290    then y = 121.31 degrees             and      -58.69  (301.31) degrees

then cos (y)  =               -.5196                        and       +.5196    

 Apr 20, 2018
 #3
avatar+99391 
+1

 

If x = arctan(-1/5) and x + y = 290 degrees, then cos y

 

Firstly I find it totally confusing to call angles x and y.

So I am going to replace x with theta and y with alpha.

I am also going to assume that both the angles are positive and between 0 and 290.

\(tan\theta<0\)   therefore theta must be in the 2nd or 4th quadrant but only the second one will work.

 

 

 


\(\alpha=290-\theta\\ cos(\alpha)\\ =cos(290-\theta)\\ =cos290cos\theta+sin290sin\theta\\ =cos70cos\theta  -sin70sin\theta\\ =cos70\times \frac{-5}{\sqrt{26}}  -sin70\times \frac{1}{\sqrt{26}}\\ = \frac{-5cos70-sin70}{\sqrt{26}} \\ \approx 0.5197\)

.
 Apr 20, 2018

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