SOLUTION: Hi I got a unit test back and bombed this question. Solve 2 sin^2 theta - 7 sin theta = -3, where 0 degrees < theta < or = to 360 degrees. Could you please explain the steps so I

Algebra ->  Trigonometry-basics -> SOLUTION: Hi I got a unit test back and bombed this question. Solve 2 sin^2 theta - 7 sin theta = -3, where 0 degrees < theta < or = to 360 degrees. Could you please explain the steps so I       Log On


   

Question 278428: Hi I got a unit test back and bombed this question. Solve 2 sin^2 theta - 7 sin theta = -3, where 0 degrees < theta < or = to 360 degrees. Could you please explain the steps so I have a chance on the re-test. Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we let , we can substitute to get 2z%5E2-7z=-3. Add 3 to both sides to get 2z%5E2-7z%2B3=0.

Now use the quadratic formula to solve for 'z'. It turns out that the solutions in terms of 'z' are z=1%2F2 or z=3


Since we let , this means that or . However, recall that the max value of sine is 1 (use the unit circle to see this). So 3 is not in the range of sine. So has no solutions. This means that we can ignore it and focus on solving


--------------------------------------------

... Start with the given equation


... Take the inverse sine of both sides to eliminate the sine on the left side.


or ... Now evaluate the inverse sine of 1%2F2 to get either 30 or 150 degrees. Don't forget to add the term to include all solutions.

Now because , this means that we've hit all of the possible solutions since adding 360 to any solution will land us outside the given interval. So we can simply say that the solutions are:

or

where both solutions are in degrees.