How do you do simplify cos [sec ^-1 (-5)]?

1 Answer
Nov 6, 2015

-1/5

Explanation:

cos[sec^-1(-5)]

Finding the value of the Composition:

Lets being to solve the equation by working on the inside. Immediately we can see that sec^-1(5/(-1)) isn't a special angle. If you noticed how I attached the negative sign to "1" is because sec = r/x. The radius can not be negative. and "1" serves as the x-value in this equation.

Note: The inverse of cosine (secant) is restricted between 0 < x < pi. (This would matter if it were asking for sin instead of cos because the y-value would become negative and give you a wrong answer).
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Now cosine is x/r. So simply put the values where they belong.

cos((-1)/5) = -1/5

This is not a special angle so leave the answer as a improper fraction or decimal. Whatever your instructor prefers. :)