SOLUTION: Find all degree solutions in the interval 0 &#8804; &#952; < 360. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the sol

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Question 1016305: Find all degree solutions in the interval 0 ≤ θ < 360. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.)
8 cos(theta) + 10 tan(theta) = sec(theta)

Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
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Find all degree solutions in the interval 0 ≤ θ < 360. If rounding is necessary, round to the nearest tenth of a degree.
Use your graphing calculator to verify the solution graphically. (Enter your answers as a comma-separated list.)
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 = ,

 = ,    <----- multiply both sides by . You will get

 = ,       <-----  replace   by  

 = ,

 = ,

 = .

Now introduce new variable x =  for brevity. Then the last equation takes the form

 = .

Solve this quadratic equation using the quadratic formula. You will get the roots

 =  and  = .

First root doesn't fit, since it is greater than 1. 
Only the root x =  fits.

Thus  = .

Hence,  = 210 or  = 330.

Answer.  = 210 or  = 330.


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