SOLUTION: If 0<A<pi/2 and sin A + 1= 2 sqrt(1-sin^2(A)), determine the value of sinA

Algebra ->  Trigonometry-basics -> SOLUTION: If 0<A<pi/2 and sin A + 1= 2 sqrt(1-sin^2(A)), determine the value of sinA      Log On


   

Question 1153087: If 0
Found 3 solutions by josgarithmetic, greenestamps, Alan3354:
Answer by josgarithmetic(39625) About Me  (Show Source):
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If 0
No. The way you did that breaks the rendering.
If 0

What you tried to show is this:


If 0 leftarrow A leftarrow pi/2 and sin A + 1= 2 sqrt(1-sin^2(A)), determine the value of sinA







Written better, you probably have:

If 0%3CA%3Cpi%2F2 and sin%28A%29%2B1=2%2Asqrt%281-sin%5E2%28A%29%29, determine the value of  sin%28A%29.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


sin%28A%29%2B1=2%2Asqrt%281-sin%5E2%28A%29%29

Square both sides:

sin%5E2%28A%29%2B2%2Asin%28A%29%2B1+=+4%281-sin%5E2%28A%29%29+=+4-4sin%5E2%28A%29

5sin%5E2%28A%29%2B2sin%28A%29-3+=+0

Solve the quadratic equation by factoring:

%285sin%28A%29-3%29%28sin%28A%29%2B1%29+=+0

sin%28A%29+=+3%2F5 OR sin%28A%29+=+-1

The restriction 0%3CA%3Cpi%2F2 means sin(A) has to be between 0 and 1, so....

ANSWER: sin(A) = 3/5

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If 0 -------------
Put spaces around the < signs.
If 0 < A < pi/2 and sin A + 1= 2 sqrt(1-sin^2(A)), determine the value of sin(A)
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Use parentheses for sin(A)