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On the unit circle, an angle terminates at the coordinate (x,y). What is the relationship between the x and y components of the coordinate and the trig functions sin and cos?How can we use those relationships to predict the sign (+/-) for these trig functions when an angle terminates within a given quadrant?

On the unit circle an angle terminates at the coordinate xy What is the relationship between the x and y components of the coordinate and the trig functions sin class=

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The unit circle is represented below:

As can be observed in the figure above, for an angle (t), the relation between the trigonometric functions and x and y components is:

x = cos(t)

y = sen(t)

x is positive in the first and in the fourth quadrant. Thus, cos (t) will be positive for angles in the first and fourth quadrant.

y is positive in the first and in the second quadrant. Thus, sin (t) will be positive for angles in the first and second quadrant.

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