Demonstrate that sin 6 < 0 .

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know that the number pi=3.14 (approx.), so, if we'll calculate:

 2pi=6.28 and 2*pi-pi/2=(3*pi)/2=1.5*pi=4.71

From the results above, 6 belongs to the interval (3pi/2,2pi), meaning 6 is in the IV-th quadrant.

In the IV-th quadrant, sine function is negative, so sin 6<0.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

sin 6 = sin(6radian)

= sin (6*180/pi) = sin (sin 343.77...) = sin (-16.225..)

= -sin (16.225..). But sin16.225 nbeing in first quadrant is positive. Therefore, sin (6radians) is negative.

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