document.write( "Question 494833: Please help me with this problem. I need to find the exact value of this expression without using a calculator:
\n" ); document.write( " $\"+sec%28sin%5E-1%28-1%2F5%29%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #335982 by lwsshak3(11628) $\"\"$ $\"About$

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Please help me with this problem. I need to find the exact value of this expression without using a calculator. sec(sin^-1(-1/5))
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\n" ); document.write( "sin^-1(-1/5)
\n" ); document.write( "This is an angle whose sin=-1/5 which means the reference angle is in quadrants III or IV where sin<0. You are working with a right triangle where the opposite side is negative 1 and the hypotenuse=5, which means the adjacent side =√24 in quadrant IV and -√24 in quadrant III. So cos=√24/5 or -√24/5 depending which quadrant is specified. Sec of the angle, being the reciprocal of cos, would be 5/√24 or -5/√24
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\n" ); document.write( "sec(sin^-1(-1/5))=5/√24 or -5/√24 \n" ); document.write( "

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