# The Trigo Dilemma

Given that sinA= $$\frac{-1}{\sqrt{5}}$$ 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:

$$\frac{-2}{\sqrt{5}}$$

With Calculator,

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

$$\frac{2}{\sqrt{5}}$$

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

Hurkyl
Staff Emeritus
Gold Member
With Calculator,

A= Inverse Sin($$\frac{-1}{\sqrt{5}}$$) = -26.57 (4 T.C.)
That angle very clearly does not satisfy the system of equations and inequalities you were trying to solve....

Then is it possible to get Angle A?

verty
Homework Helper
Yes, it is possible. Think about the domain and range of the arcsin function, then use trigonometric identities to get the correct answer.

mathman
A= -26.57 (4 T.C.)

I'll assume A is in degrees. That angle is in the fourth quadrant, not the third.