Thread: Limits with trig values

I'm having trouble with my AP Calculus homework dealing with trig limits. I get these long values and have no idea how to reduce them.

Example:

Limit as x approaches zero of cot(3x)/csc(2x)

I understand the first part:

Lim x->0 (cos(3x)/sin(3x))/(1/sinx)

which reduces to:

Lim x -> 0 (cos(3x)sin(x))/sin(3x)

but I'm at a loss of where to go from here. Everything I try either becomes so complicated I don't know what to do with it or ends up as 0/0. Thanks in advance to anyone who can shed some light on this dilemma.

Originally Posted by oObutterfly-chaserOo

I'm having trouble with my AP Calculus homework dealing with trig limits. I get these long values and have no idea how to reduce them.

Example:

Limit as x approaches zero of cot(3x)/csc(2x)

I understand the first part:

Lim x->0 (cos(3x)/sin(3x))/(1/sinx)

which reduces to:

Lim x -> 0 (cos(3x)sin(x))/sin(3x)

but I'm at a loss of where to go from here. Everything I try either becomes so complicated I don't know what to do with it or ends up as 0/0. Thanks in advance to anyone who can shed some light on this dilemma.

Hopefully you know that for all


using this fact and some trig identities



Now multiply both the numerator and denominator by 6x to get



using the above we get

Originally Posted by oObutterfly-chaserOo

I'm having trouble with my AP Calculus homework dealing with trig limits. I get these long values and have no idea how to reduce them.

Example:

Limit as x approaches zero of cot(3x)/csc(2x)

I understand the first part:

Lim x->0 (cos(3x)/sin(3x))/(1/sinx)

which reduces to:

Lim x -> 0 (cos(3x)sin(x))/sin(3x)

but I'm at a loss of where to go from here. Everything I try either becomes so complicated I don't know what to do with it or ends up as 0/0. Thanks in advance to anyone who can shed some light on this dilemma.

L'Hospital's Rule works quite nicely here, since your limit is of the indeterminate form .






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