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

#2**+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**+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