why is cot 180 undefined

why is cot 180 undefined We learned that cotangent is the reciprocal of the tangent function and that cot 180 degrees is undefined because the tangent of 180 degrees is undefined Remember that each angle has

Trigonometric functions are equal to 0 1 1 or undefined when the angle lies on an axis meaning that the angle is equal to 0 90 180 or 270 degrees 0 pi 2 pi or 3 pi 2 in radians As the value of sin approaches zero and the value of cos approaches one however the value of cot tends to infinity The value of cot when cos equals one is thus said to be undefined As mentioned the tangent

why is cot 180 undefined

cos-90-theta-sec-theta-tan-180-theta-sin-360-theta-sec-180

why is cot 180 undefined
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Let x be the value equal to c o t 180 x c o t 180 co t 180 0 co t 0 c o t 180 a c o ta cos 0 sin 0 c o t c o s s i n 1 0 c o s 0 1 s i n 0 0 That s undefined because as you approach 90 from either direction tan approaches positive or negative infinity cot 90 hence approaches 1 infinity either positive or negative

Why we say tan pi 2 is undefined Since frac sin pi 2 cos pi 2 and cos pi 2 0 we should say tan pi 2 is undefined Note that frac 0 always is undefined By this same logic sin 0 would not be defined because sin 0 1 csc 0 and csc 0 1 0 is undefined But sin 0 like cot 90 is perfectly well defined and equal to 0

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Rewrite cot 180 cot 180 in terms of sines and cosines Apply the reference angle by finding the angle with equivalent trig values in the first quadrant The exact value of sin 0 sin 0 is 0 Remember that cot theta 1 tan theta cos theta sin theta and note that the sine of a 180 degree angle is zero and the cosine of that angle is 1 So this evaluates to

To find cot180 csc180 sec180 cot180 cot 1 tan 1 0 csc180 csc 1 sin 1 0 sec180 sec 1 cos 1 1 1 Rewrite cot 180 cot 180 in terms of sines and cosines Apply the reference angle by finding the angle with equivalent trig values in the first quadrant The exact value of sin 0 sin 0 is 0

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why is cot 180 undefined - Let x be the value equal to c o t 180 x c o t 180 co t 180 0 co t 0 c o t 180 a c o ta cos 0 sin 0 c o t c o s s i n 1 0 c o s 0 1 s i n 0 0