SOLUTION: This is a 3-part question.
1) Solve the following equation. Which of its values from the interval 0-180 degrees are correct? sin^2a + 1.5sina = 1
a) 30 degrees, 150 degrees
Algebra.Com
Question 767520: This is a 3-part question.
1) Solve the following equation. Which of its values from the interval 0-180 degrees are correct? sin^2a + 1.5sina = 1
a) 30 degrees, 150 degrees; b) 45 degrees, 120 degrees; c) 60 degrees, 150 degrees; d) 30 degrees, 110 degrees.
2) Why can't we use the solution sina = -2 of the equation?
3) Solve also the equation sin^2a - 1.5sina = 1.
I do not know how to even begin to solve this problem. If you are unable to help me, could you recommend where I might look for help as I cannot find anything about it on the Internet.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ +\ 1.5\sin(a)\ =\ 1)
Let )
, then
Solve the quadratic, which factors:
\left(u\ -\ \frac{1}{2}\right)\ =\ 0)
Then substitute back, so
\ =\ -2)
or
\ =\ \frac{1}{2})
Discard the 
root because the range of the 
function is 
Using the unit circle:
The value of 
for an angle is the 
-coordinate of the point of intersection of the terminal ray of the angle and the unit circle. So find the two points in the desired interval where the -coordinate equals 
Solve your other problem the same way, but you might want to reconsider the interval for your solutions if you are going to have any solutions at all.
John
My calculator said it, I believe it, that settles it
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