Trigonometric Limits

Trigonometric Limits

more examples of limits

Substitution Theorem for Trigonometric Functions

laws for evaluating limits

Theorem A. For each point c in function's domain:

lim sin x = sin c,

xc

lim tan x = tan c,

xc

lim csc x = csc c,

xc

lim cos x = cos c,

xc

lim cot x = cot c,

xc

lim sec x = sec c.

xc

Theorem A. For each point c in function's domain:

lim sin x = sin c,

xc

lim tan x = tan c,

xc

lim csc x = csc c,

xc

lim cos x = cos c,

xc

lim cot x = cot c,

xc

lim sec x = sec c.

xc

Proof. Prove first that

lim sin x = 0,

x0

lim cos x = 1.

x0

Is it obvious? lim sin x = 0,

x0

lim cos x = 1.

x0

y=sin(x)

y=cos(x)

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