Thread: Help with trig algebra. I can't figure this out

Ok, so I am looking at the min and max for the angle x:

-12cos(x) + (2)12sin(x) = 5

and

-12cos(x) + (2)12sin(x) = -5

which I reduced to:

(12)(2sin(x) - cos(x)) = ±5

2sin(x) - cos(x) = ±5/12

I'm not sure how to solve for the angle (x) from here.

Originally Posted by mathdude09

Ok, so I am looking at the min and max for the angle x:

-12cos(x) + (2)12sin(x) = 5

and

-12cos(x) + (2)12sin(x) = -5

which I reduced to:

(12)(2sin(x) - cos(x)) = ±5

2sin(x) - cos(x) = ±5/12

I'm not sure how to solve for the angle (x) from here.

I'm not sure about what is going on here, but:







Squaring both sides




Now you have a quadratic in .

Can you solve quadratics?

Working with what you gave me I was able to successfully get both angles using the quadratic formula, thanks.

Just to understand exactly how you manipulated the sin function:

sin(x) = sqrt(1-cos(x)^2) ???

Is there a listing of these conversions somewhere?

Originally Posted by mathdude09

Working with what you gave me I was able to successfully get both angles using the quadratic formula, thanks.

Just to understand exactly how you manipulated the sin function:

sin(x) = sqrt(1-cos(x)^2) ???

Is there a listing of these conversions somewhere?

This was derived from the pythagorean identity IE



Subtracting...

Oh yeah. Pythagoras, unit circle...it's all coming back now. Thanks