SOLUTION: 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)) }}}

Algebra ->  Trigonometry-basics -> SOLUTION: 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)) }}}      Log On


   

Question 494833: Please help me with this problem. I need to find the exact value of this expression without using a calculator:
+sec%28sin%5E-1%28-1%2F5%29%29+
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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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sin^-1(-1/5)
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
Ans:
sec(sin^-1(-1/5))=5/√24 or -5/√24