document.write( "Question 623876: find the other five functions of acute angle A,given that cscA=4 over 3
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Algebra.Com's Answer #392381 by jsmallt9(3758) $\"\"$ $\"About$

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To better understand how this works, let's draw a diagram:

Draw a right triangle. (It doesn't matter how it looks.)
Choose one of the acute angles in the triangle and label it A.
Since the csc ratio is hypotenuse/opposite and since we want A to have a csc of 4/3, label the hypotenuse of the triangle (opposite the right angle) with a length of 4 and label the length of the side opposite angle A with a length of 3.

To find all five of the other functions, we will need the adjacent side, too. Since we have two of the three sides of the triangle, we can use the Pythagorean Theorem to find it. Let's call the adjacent side \"b\". Inserting \"b\" and 4 and 3 into the Pythagorean equation we get:
\n" ); document.write( " $\"4%5E2+=+3%5E2+%2B+b%5E2\"$
\n" ); document.write( "Solving for b:
\n" ); document.write( " $\"16+=+9+%2B+b%5E2\"$
\n" ); document.write( " $\"7+=+b%5E2\"$
\n" ); document.write( " $\"sqrt%287%29+=+b\"$ (ignoring the negative square root since lengths of the sides of triangles cannot be negative)

\n" ); document.write( "Now we can find the other 5 functions, using 4 for the hypotenuse, 3 for the opposite side and $\"sqrt%287%29\"$ for the adjacent side:
\n" ); document.write( " $\"sin%28A%29+=+3%2F4\"$
\n" ); document.write( " $\"cos%28A%29+=+sqrt%287%29%2F4\"$
\n" ); document.write( " $\"tan%28A%29+=+3%2Fsqrt%287%29\"$
\n" ); document.write( " $\"sec%28A%29+=+4%2Fsqrt%287%29\"$
\n" ); document.write( " $\"cot%28A%29+=+sqrt%287%29%2F3\"$

\n" ); document.write( "We don;t usually leave square roots in denominators so we should rationalize tan and sec:
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