+0

# Another trig problem

0
281
3
+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
+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
+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.

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

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Apr 20, 2018