document.write( "Question 618255: the question is find the exact value of sin theta if cos theta=5/7 and theta terminates in quadrant 4. Draw the angle theta in standard position and the exact valu of sin theta?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #388780 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
We can use $\"sin%5E2%28theta%29+=+1+-+cos%5E2%28theta%29\"$ and the fact that $\"theta\"$ terminates in the 4th quadrant to find $\"sin%28theta%29\"$ .

\n" ); document.write( " $\"sin%5E2%28theta%29+=+1+-+cos%5E2%28theta%29\"$
\n" ); document.write( "Inserting the given value for $\"cos%28theta%29\"$ :
\n" ); document.write( " $\"sin%5E2%28theta%29+=+1+-+%285%2F7%29%5E2\"$
\n" ); document.write( "Simplifying...
\n" ); document.write( " $\"sin%5E2%28theta%29+=+1+-+25%2F49\"$
\n" ); document.write( " $\"sin%5E2%28theta%29+=+49%2F49+-+25%2F49\"$
\n" ); document.write( " $\"sin%5E2%28theta%29+=+24%2F49\"$
\n" ); document.write( "So $\"sin%28theta%29\"$ is one of the square roots of 24/49. Since $\"theta\"$ terminates in the 4th quadrant and since sin is negative in the 4th quadrant, we know to use the negative square root:
\n" ); document.write( " $\"sin%28theta%29+=+-sqrt%2824%2F49%29\"$
\n" ); document.write( "which simplifies:
\n" ); document.write( " $\"sin%28theta%29+=+-sqrt%2824%29%2Fsqrt%2849%29\"$
\n" ); document.write( " $\"sin%28theta%29+=+-sqrt%284%2A6%29%2F7\"$
\n" ); document.write( " $\"sin%28theta%29+=+-%28sqrt%284%29%2Asqrt%286%29%29%2F7\"$
\n" ); document.write( " $\"sin%28theta%29+=+-%282%2Asqrt%286%29%29%2F7\"$

\n" ); document.write( "I'll leave the drawing up to you. \n" ); document.write( "

\n" );