+0  
 
0
64
3
avatar+66 

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. 

SurpriseMe  Apr 19, 2018
edited by SurpriseMe  Apr 20, 2018
Sort: 

2+0 Answers

 #2
avatar+12266 
+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    

ElectricPavlov  Apr 20, 2018
 #3
avatar+92437 
+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.

 

 

 


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

Melody  Apr 20, 2018

19 Online Users

avatar
avatar
avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy