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25sinxcosx-5sinx+20cosx=4

Guest Mar 3, 2015

Best Answer 

 #3
avatar+87301 
+5

Very nice, Anonymous.....

25sinxcosx-5sinx+20cosx= 4

Following your lead....

25sinxcosx + 20cosx = 4 + 5sinx

5cosx(5sinx + 4) = (5six + 4)

5cosx = 1

cosx =1/5  at 78.46°

And the other value where sin x = (-4/5) is  about 233°

So...that's all our angles on [0,360]

 

CPhill  Mar 3, 2015
 #1
avatar+87301 
+5

 

 

25sinxcosx-5sinx+20cosx= 4

Maybe someone else can solve this one by some algebraic means......but here's a graphical solution.........https://www.desmos.com/calculator/bdgkyrfxh1

It looks like the "x's" that make this true are at 78.5°, 233.1° and 306.9° on the interval [0, 360]

 

CPhill  Mar 3, 2015
 #2
avatar
+5

Partially:

25sinxcosx-5sinx+20cosx=4

5sinx(5cosx-1)=4-20cosx

5sinx= -4(5cosx-1)/ (5cosx-1)

5sinx=-4

sinx=-4/5  which is 306.9 degrees.

 

I have difficulty with the other values (sleepy).

Guest Mar 3, 2015
 #3
avatar+87301 
+5
Best Answer

Very nice, Anonymous.....

25sinxcosx-5sinx+20cosx= 4

Following your lead....

25sinxcosx + 20cosx = 4 + 5sinx

5cosx(5sinx + 4) = (5six + 4)

5cosx = 1

cosx =1/5  at 78.46°

And the other value where sin x = (-4/5) is  about 233°

So...that's all our angles on [0,360]

 

CPhill  Mar 3, 2015

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