Question 689854
what is the relationship between cotangent theta and cotangent NEGATIVE theta?
cot(x)=-cot(-x) (this is called an odd function, compared to an even function)
Examples:
pick angle of 45º in quadrant I
this gives you a reference angle of 45º where cot 45º=1
-45º will also give you a reference angle of 45º but in quadrant IV where cot -45=-1
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pick angle 135º in quadrant II
this gives you a reference angle of 45º where cot135º=-1
-135º will also give you a reference angle of 45º but in quadrant III where cot-135º=1
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pick angle 225º in quadrant III
this gives you a reference angle of 45º where cot225º=1
-225º will also give you a reference angle of 45º but in quadrant II where cot-225º=-1
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note: I used a reference angle of 45º for the examples but this will hold true for any reference angle.
This will also hold true for the tan function since cot is the reciprocal of tan.
A negative angle means rotating in a clockwise direction and a positive angle in a counter-clockwise direction.The value for the trig functions and their reciprocals is computed from the reference angle and the sign depends on which of the 4 quadrants the angle is in. See if you can apply this method to the sin and cos functions.
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Hope this helps!