SOLUTION: if x is the measure of a positive acute angle and cos x= 7/32 find the value of sin 1/2x

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Question 615505: if x is the measure of a positive acute angle and cos x= 7/32 find the value of sin 1/2x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since x is a positive acute angle then (1/2)x is also a positive acute angle. And if (1/2)x is a positive acute angle then sin((1/2)x) will be positive. This is important to determine because the formula for sin((1/2)x) has a "plus or minus" symbol in it. When you use that formula you have to figure out whether to use the positive square root or the negative one. We now know to use the positive square root:
sin%28%281%2F2%29x%29+=+sqrt%28%281-cos%28x%29%29%2F2%29
Substituting in the given value for cos(x) we get:
sin%28%281%2F2%29x%29+=+sqrt%28%281-%287%2F32%29%29%2F2%29
Simplifying...
sin%28%281%2F2%29x%29+=+sqrt%28%2832%2F32-%287%2F32%29%29%2F2%29
sin%28%281%2F2%29x%29+=+sqrt%28%2825%2F32%29%2F2%29
sin%28%281%2F2%29x%29+=+sqrt%2825%2F64%29
sin%28%281%2F2%29x%29+=+sqrt%2825%29%2Fsqrt%2864%29
sin%28%281%2F2%29x%29+=+5%2F8