Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 13"

Revision as of 12:22, 23 July 2006

Suppose that $x$ and $y$ are numbers such that $\sin(x+y) = 0.3$ and $\sin(x-y) = 0.5$ . Then $\sin (x)\cdot \cos (y) =$

$\mathrm{(A) \ }0.1 \qquad \mathrm{(B) \ }0.3 \qquad \mathrm{(C) \ }0.4 \qquad \mathrm{(D) \ }0.5 \qquad \mathrm{(E) \ }0.6$

Expanding $\sin{(x+y)}$ and $\sin{(x-y)}$ , we have: $(1)$ $\sin{x}\cos{y}+\sin{y}\cos{x}=.3$ $(2)$ $\sin{x}\cos{y}-\sin{y}\cos{x}=.5$

$(1)+(2)$ yields $2\sin{x}\cos{y}=.8$ and our answer is $.4$ .

@@ Line 11: / Line 11: @@
 <math>(1)+(2)</math> yields <math>2\sin{x}\cos{y}=.8</math> and our answer is <math>.4</math>.
-== See also ==
+----
-* [[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]]