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

Mathematics
Tutor: None Selected Time limit: 1 Day

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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
May 2nd, 2015
...
May 2nd, 2015
May 27th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer