Question 508364: sec(sin^-1 x/(x ^2+4))
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! sec(sin^-1 x/(x ^2+4))
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What this problem is asking, is to find the secant of an angle (call it A) whose sin= x/(x ^2+4)
To solve given problem, find the cosine of A then take its reciprocal to get its secant.
What we have here is a right triangle with side opposite angle A=x and the hypotenuse=(x^2+4). To solve given problem, we must find the adjacent side in terms of x.
We can use the trig identity: sin^2+cos^2=1 or Pythagorean Theorem. Let's use the latter:
Adjacent side=sqrt(hypotenuse^2-opposite side^2)
Adjacent side=sqrt[(x^2+4)^2-x^2]
=sqrt[(x^4+8x^2+16)^2-x^2]
=sqrt[x^4+7x^2+16]
cosA=[sqrt(x^4+7x^2+16)]/(x^2+4)
sec(sin^-1 x/(x ^2+4))=(x^2+4)/[sqrt(x^4+7x^2+16)]
Remember: The inverse of a trig function is always equal to an angle and the trig function is always equal to a value or number.
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