Conditional Trigonometric Identities
Conditional Trigonometric Identities - In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a cer..
Conditional Trigonometric Identities - In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a cer..Conditional Trigonometric Identities
In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relationship exists among the angles considered. Many interestin..
In the previous sections many identities have been discussed. They are true for all values of the angles for which trigonometric functions are defined. In this section we prove identities, where a certain relationship exists among the angles considered. Many interestin.. rotate it for other possible views involve math on/in a sphere. Spherical math/rotating involves using trig functions in various mathematical relationships, including division. Unfortunately, all trig functions have an angle for which the value of the function is zero. Dividing by zero is described as undefined. But, in fact, few functions are truly undefined when the denominator is zero; that's when we use the "limit" idea. You know, the limit of such and such as the denominator ...
rotate it for other possible views involve math on/in a sphere. Spherical math/rotating involves using trig functions in various mathematical relationships, including division. Unfortunately, all trig functions have an angle for which the value of the function is zero. Dividing by zero is described as undefined. But, in fact, few functions are truly undefined when the denominator is zero; that's when we use the "limit" idea. You know, the limit of such and such as the denominator ...
Question : there are 2 types of equations: identity & conditional
from what I've learned,the equation is identity if all of the elements of the domain are solutions of the equation. And it's conditional if AT LEAST ONE element of the domain is not a solution or UNDEFINED...
how 'bout: cos x tan x = sin x??
...if x is 90 or 270 or 450 degrees, the equation in the left-hand is undefined...but,based from the book I've read,it's an IDENTITY!...
so,is it really identity or conditional??
subject: Trigon..
Answer : First of all, it is an identity - this means it is tru for all x; and in this case we can prove it, since tan(x) = sin(x)/cos(x), tan(x)cos(x) = cos(x)*sin(x)/cos(x) = sin(x). You are correct that tan(x) is undefined at points x = 90, 270, etc; but we also need to consider the cosine that it is multiplied by - work out the limit of the function: lim(as x goes to 90) [tan(x)*cos(x)] = lim(as x goes to 90) [((sin(x)/cos(x))*cos(x)] = lim(as x goes to 90) [(sin(x)*cos(x))/cos(x)] L'hopital's rule says that if we have limits in e.g. lim (as x goes to c) [f(x)/g(x)], where f(c) = 0 and g(c) = 0, then lim (as x goes to c) [f(x)/g(x)] = lim (as x goes to c) [f'(x)/g'(x)], where f'(x) and g'(x) are the derivatives. We can use it here since sin(90)*cos(90) = 0*1 = 0, and cos(90) = 0. We notice that sin(x)cos(x) = (1/2)*sin(2x), so the limit is = lim(as x goes to 90) [((1/2)*sin(2x))/cos(x)] And taking derivatives of top and bottom with l'hopital's rule .... More from Yahoo Answers
Answer : First of all, it is an identity - this means it is tru for all x; and in this case we can prove it, since tan(x) = sin(x)/cos(x), tan(x)cos(x) = cos(x)*sin(x)/cos(x) = sin(x). You are correct that tan(x) is undefined at points x = 90, 270, etc; but we also need to consider the cosine that it is multiplied by - work out the limit of the function: lim(as x goes to 90) [tan(x)*cos(x)] = lim(as x goes to 90) [((sin(x)/cos(x))*cos(x)] = lim(as x goes to 90) [(sin(x)*cos(x))/cos(x)] L'hopital's rule says that if we have limits in e.g. lim (as x goes to c) [f(x)/g(x)], where f(c) = 0 and g(c) = 0, then lim (as x goes to c) [f(x)/g(x)] = lim (as x goes to c) [f'(x)/g'(x)], where f'(x) and g'(x) are the derivatives. We can use it here since sin(90)*cos(90) = 0*1 = 0, and cos(90) = 0. We notice that sin(x)cos(x) = (1/2)*sin(2x), so the limit is = lim(as x goes to 90) [((1/2)*sin(2x))/cos(x)] And taking derivatives of top and bottom with l'hopital's rule .... More from Yahoo Answers
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