quadrants is it really important to say in what quadrant the angle is?

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Yest it is important. When we know that location of the angle, we can determine the values of the trigonometric identities.

For example:

We will compare the angle pi/3 into the first, second, third, and 4th quadrants.

If pi/3 is in the 1st quadrant:

==> cos(pi/3) = 0.5

If pi/3...

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Yest it is important. When we know that location of the angle, we can determine the values of the trigonometric identities.

For example:

We will compare the angle pi/3 into the first, second, third, and 4th quadrants.

If pi/3 is in the 1st quadrant:

==> cos(pi/3) = 0.5

If pi/3 is in the 2nd quadrant:

==> pi/3 = pi - pi/3 = 2pi/3

==> cos (2pi/3) = - 0.5

If pi/3 is in the 3rd quadrant.

==> pi/3 = pi + pi/3 = 4pi/3

==> cos(4pi/3) = - 0.5

If pi/3 is in the 4th quadrant:

==> pi/3 = 2pi - pi/3 = 5pi/3

==> cos( 5pi/3) = 0.5

Then, we notice that the sign changes as the angle changes the location.

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