Question 494833
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 =&#8730;24 in quadrant IV and -&#8730;24 in quadrant III. So cos=&#8730;24/5 or -&#8730;24/5 depending which quadrant is specified. Sec of the angle, being the reciprocal of cos, would be 5/&#8730;24 or -5/&#8730;24
Ans:
sec(sin^-1(-1/5))=5/&#8730;24 or -5/&#8730;24