The Trigo Dilemma

  • Thread starter Kyoma
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  • #1
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Main Question or Discussion Point

Given that sinA= [tex]\frac{-1}{\sqrt{5}}[/tex] where A is more than 180 degrees and less than 270 degrees. Find the value of cos(-A).

Without using Calculator,

Since cos(-A) = cosA, and that A is in the 3rd quadrant, then after solving for the hypotenuse, adjacent and opposite, I got:

[tex]\frac{-2}{\sqrt{5}}[/tex]

With Calculator,

A= Inverse Sin([tex]\frac{-1}{\sqrt{5}}[/tex]) = -26.57 (4 T.C.)
Subst -26.57 into cos(-A), I got:

[tex]\frac{2}{\sqrt{5}}[/tex]

One is positive, another is negative. Which is which?
 

Answers and Replies

  • #2
Hurkyl
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With Calculator,

A= Inverse Sin([tex]\frac{-1}{\sqrt{5}}[/tex]) = -26.57 (4 T.C.)
That angle very clearly does not satisfy the system of equations and inequalities you were trying to solve....
 
  • #3
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Then is it possible to get Angle A?
 
  • #4
verty
Homework Helper
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Yes, it is possible. Think about the domain and range of the arcsin function, then use trigonometric identities to get the correct answer.
 
  • #5
mathman
Science Advisor
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A= -26.57 (4 T.C.)
I'll assume A is in degrees. That angle is in the fourth quadrant, not the third.
 

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