Trig Limit Calculator
Evaluate common trigonometric limits as x approaches 0
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Standard Trig Limit Formulas lim x->0 sin x / x = 1, lim x->0 tan x / x = 1, lim x->0 (1-cos x)/x^2 = 1/2
These formulas assume radian measure and are foundational in calculus.
⚠ Use radians for standard trigonometric limit formulas. Degree measure changes the scaling.
How Trig Limits Work Rewrite the expression to match a standard limit, then apply the known result.
Sine Limit
sin u / u approaches 1.
Tangent Limit
tan u / u also approaches 1.
Cosine Limit
(1-cos u)/u^2 approaches 1/2.
Scaling
Substitute u = kx and track powers of k.
Example: lim x->0 (1-cos(3x))/x^2 = 9/2 because u=3x gives k^2/2.
Applications Calculus Limits Derivative Proofs Small Angle Approximation Physics
Frequently Asked Questions What is the standard sine limit?▼
The standard limit is lim x->0 sin x / x = 1 when x is measured in radians.
What is the standard tangent limit?▼
The standard limit is lim x->0 tan x / x = 1 in radians.
Why must angles be in radians for trig limits?▼
The standard trigonometric limit formulas are derived using radian measure. Degree measure introduces a scaling factor.
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