Free Scientific Calculator Online (with DEG/RAD Guide)
A free online scientific calculator with trig in degrees or radians, logs, powers, roots, factorials and scientific notation, plus how to use every key.
Tag: trigonometry
Read article → Free Scientific Calculator Online (with DEG/RAD Guide)
Limit of sin(x)/x as x → 0 Equals 1: Three Proofs
lim x→0 sin(x)/x = 1. See the squeeze theorem proof, the L’Hôpital shortcut (and why it’s circular), a numerical table and related limits.
Integral of sec²(x) = tan(x) + C, with Examples
The integral of sec²(x) is tan(x) + C, because the derivative of tan x is sec²x. Examples with sec²(3x), tan²x, and definite integrals.
Integral of sin²(x): x/2 − sin(2x)/4 + C
The integral of sin²(x) is x/2 − sin(2x)/4 + C. Uses the power-reduction identity; includes cos²x, sin²(3x) and definite integrals over [0, π].
Integral of sec(x): ln|sec x + tan x| + C, Step by Step
The integral of sec(x) is ln|sec x + tan x| + C. See the multiply-by-(sec x + tan x) trick, a second method, csc x, and definite examples.
Integral of tan(x): −ln|cos x| + C Derivation
The integral of tan(x) is −ln|cos x| + C, or equivalently ln|sec x| + C. Step-by-step u-substitution, definite examples and tan²x.
Derivative of cos²(x): −sin(2x) with Two Methods
The derivative of cos²(x) is −2sin(x)cos(x) = −sin(2x). Two methods, plus sin²(x), cos(x²) and cos²(3x) worked examples.
Derivative of sec(x) = sec(x)tan(x): Proof and Examples
The derivative of sec(x) is sec(x)tan(x). See the proof from 1/cos(x), the chain rule form, second derivative and worked examples.
Derivative of tan(x) = sec²(x): Proof and Examples
The derivative of tan(x) is sec²(x). Learn the quotient rule proof, the chain rule version for tan(g(x)), and worked examples.