solve the given equation: 7sin^2 theta -22 sin theta +3 =0

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solve the given equation: 7sin^2 theta -22 sin theta +3 =0 

May 2nd, 2015

Hey there! So for this question, you are going to let sin theta=x (or whatever variable you like)

So we get:

7x^2-22x+3=0

Look familiar now?  So we can apply the quadratic formula to find x.

x=(22+-(22^2-4(7)(3))^1/2)/14

We get:

x=1/7 and x=3

Now, we back-substitute and get 

sin theta=1/7

sin theta=3

So solving for theta we get: 

theta=0.1433475689053653575950742801566183260989392131334643  (thanks to wolfram alpha for all the digits)

and, for 3, it is a special case where we get an imaginary number which is better when put into polar but I have the standard form as well:

theta= 

1.57079632679489661923132169163975144209858469968755291048747... -
1.76274717403908605046521864995958461805632065652327082150659... i
(result in radians)
r = 2.36108 (radius), theta = -48.2955° (angle)

Again thank you wolfram for copyable digits.  

Let me know if you have any questions!

May 2nd, 2015

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