Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 13"
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== Problem == | == Problem == | ||
− | Suppose that <math>x</math> and <math>y</math> are numbers such that <math>\sin(x+y) = 0.3</math> and <math>\sin(x-y) = 0.5</math>. Then <math> \sin(x) \cos(y) =</math> | + | Suppose that <math>x</math> and <math>y</math> are numbers such that <math>\sin(x+y) = 0.3</math> and <math>\sin(x-y) = 0.5</math>. Then <math> \sin (x)\cdot \cos (y) = </math> |
<center><math> \mathrm{(A) \ }0.1 \qquad \mathrm{(B) \ }0.3 \qquad \mathrm{(C) \ }0.4 \qquad \mathrm{(D) \ }0.5 \qquad \mathrm{(E) \ }0.6 </math></center> | <center><math> \mathrm{(A) \ }0.1 \qquad \mathrm{(B) \ }0.3 \qquad \mathrm{(C) \ }0.4 \qquad \mathrm{(D) \ }0.5 \qquad \mathrm{(E) \ }0.6 </math></center> | ||
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<math>(1)+(2)</math> yields <math>2\sin{x}\cos{y}=.8</math> and our answer is <math>.4</math>. | <math>(1)+(2)</math> yields <math>2\sin{x}\cos{y}=.8</math> and our answer is <math>.4</math>. | ||
− | + | ---- | |
− | * [[University of South Carolina High School Math Contest/1993 Exam]] | + | |
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 12|Previous Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 14|Next Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam|Back to Exam]] | ||
[[Category:Intermediate Trigonometry Problems]] | [[Category:Intermediate Trigonometry Problems]] |
Latest revision as of 12:22, 23 July 2006
Problem
Suppose that and are numbers such that and . Then
Solution
Expanding and , we have:
yields and our answer is .