← Squeeze Theorem and Trigonometric Limits

Advanced Trigonometric Limits Practice

Use this interactive AP Calculus AB practice to work on Advanced Trigonometric Limits with immediate answer checking.

A fully mixed stream of randomized, multi-step trig limits. Problems may require identity rewrites, algebraic factoring, cancellation, standard trigonometric limits, or several of those ideas in combination. No derivatives or L'Hôpital's Rule are needed.

Practice Type

Correct: 0Attempted: 0Accuracy: —

Find the limit.

Exact form preferred. Fractions and decimals are accepted; use √ to insert a square root, then enter its contents. Use → to move past the closing parenthesis. Typed sqrt(2) also works.

Required trig identity reference

Reciprocal / Quotient

\(\sin x=\frac1{\csc x},\quad \cos x=\frac1{\sec x},\quad \tan x=\frac1{\cot x}\)

\(\tan x=\frac{\sin x}{\cos x},\quad \cot x=\frac{\cos x}{\sin x}\)

Pythagorean

\(\sin^2x+\cos^2x=1\)

\(1+\tan^2x=\sec^2x,\quad 1+\cot^2x=\csc^2x\)

Double Angle / Power Reduction

\(\sin 2x=2\sin x\cos x\)

\(\cos 2x=\cos^2x-\sin^2x=1-2\sin^2x=2\cos^2x-1\)

\(\sin^2x=\frac12(1-\cos 2x),\quad \cos^2x=\frac12(1+\cos 2x)\)

Even / Odd

\(\sin(-x)=-\sin x,\quad \cos(-x)=\cos x,\quad \tan(-x)=-\tan x\)

\(\csc(-x)=-\csc x,\quad \sec(-x)=\sec x,\quad \cot(-x)=-\cot x\)